Light of wavelength 549 nm is used to illuminate normally two glass plates 24.6 cm in length that touch at one end and are separated at the other by a wire of radius 0.025 mm. How many bright fringes appear along the total length of the plates.

The fundamental frequency of the sound produced by the average human vocal cord is approximately 11,333 Hz.

we'll need to use the formula for the fundamental frequency of a wave on a string fixed at both ends:

f1 = v / 2L

where f1 is the fundamental frequency, v is the speed of the wave, and L is the length of the string (in this case, the vocal cord).

For humans, the speed of sound in vocal cords is approximately 340 m/s. Given the average length of a vocal cord is 15 mm (0.015 m), we can now calculate the fundamental frequency:

f1 = (340 m/s) / (2 * 0.015 m) = 340 / 0.03 = 11,333 Hz

So, the fundamental frequency of the sound produced by the average human vocal cord is approximately 11,333 Hz.

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Rotating the polarizer will cause the light intensity to vary between maximum and minimum levels.

When light from an incandescent bulb, which is unpolarized, passes through a polarizer, it becomes polarized. As you rotate the polarizer between the lit bulb and your eye, you will observe the light's intensity changing. This is because the polarizer only allows light waves vibrating in a specific direction to pass through, while blocking other directions. When the polarizer is aligned with the light's vibration direction, maximum intensity is observed, and when perpendicular, minimum intensity is seen.

In summary, rotating the polarizer will cause the light intensity to vary between maximum and minimum levels.

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The distance to Jakondah would remain the same at 20 light-years, as the speed of light doesn't affect distances.

While it may seem intuitive that doubling the speed of light would affect the distance to Jakondah, it's essential to understand that light-years measure distance, not time.

A light-year is the distance that light travels in a vacuum in one year.

Therefore, even if the speed of light were to double, the actual distance between Earth and Jakondah would remain the same, at 20 light-years.

However, it's worth noting that if the speed of light were indeed doubled, light from Jakondah would reach us in half the time it currently takes.

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The new de Broglie wavelength (λ') is equal to the original wavelength (λ) when the kinetic energy of the particle doubles, assuming relativistic effects can be ignored

The de Broglie wavelength of a particle is given by the equation:λ = h / p

where λ is the de Broglie wavelength, h is the Planck constant, and p is the momentum of the particle.

Since the kinetic energy (K) of the particle is doubled, we can write:K' = 2K

The kinetic energy of a particle is related to its momentum as:K = p^2 / (2m) where m is the mass of the particle.

Substituting this expression for kinetic energy into the equation for doubling the kinetic energy:2K = p'^2 / m

Here, p' is the new momentum of the particle.

We can rewrite the expression for the de Broglie wavelength using the momentum:λ' = h / p'

We want to find the new de Broglie wavelength (λ'), so we need to relate the new momentum (p') to the original momentum (p) and find the relation between the wavelengths (λ' and λ)

From the equation for the doubled kinetic energy:2K = p'^2 / m

We can rewrite this as:p'^2 = 2Km

Taking the square root of both sides:p' = √(2Km)

Now, we can substitute this expression for p' into the equation for the de Broglie wavelength:λ' = h / p'= h / √(2Km)

Finally, we can relate the new wavelength (λ') to the original wavelength (λ) by dividing the two equations:λ' / λ = (h / √(2Km)) / (h / p)= p / √(2Km)

Since relativistic effects are ignored, we can assume that p is given by the non-relativistic momentum formula:p = √(2Km)

Therefore, we have:λ' / λ = √(2Km) / √(2Km)= 1

This means that the new de Broglie wavelength (λ') is equal to the original wavelength (λ) when the kinetic energy of the particle doubles, assuming relativistic effects can be ignored.

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A vertical magnetic field of 0.392 T is required to keep the metal rod moving at a constant speed.

When a current-carrying metal rod moves in a magnetic field, a force is exerted on it due to the interaction between the magnetic field and the current. In this case, the metal rod is gliding on two horizontal rails, and the force due to the magnetic field is required to balance the force of friction and keep the rod moving at a constant speed.

The force due to the magnetic field can be calculated using the equation:

F = BIL

where F is the force, B is the magnetic field, I is the current, and L is the length of the rod.

The force of friction can be calculated using the equation:

f = μN

where f is the force of friction, μ is the coefficient of kinetic friction, and N is the normal force.

Since the rod is moving at a constant speed, the forces due to the magnetic field and friction are equal in magnitude and opposite in direction. Therefore, we can set the two equations equal to each other:

BIL = μN

The normal force is equal to the weight of the rod, which can be calculated using:

N = mg

where m is the mass of the rod and g is the acceleration due to gravity.

Substituting the expressions for N and rearranging the equation, we get:

B = μmg/IL

Substituting the given values, we get:

B = (0.100)(0.200 kg)(9.81 m/s²)/(10.0 A)(0.500 m)

B = 0.392 T

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The actual current that can flow due to light irradiation would be lower than 1.6 A, depending on the EQE of the material.

The maximum current that can flow due to light irradiation depends on the efficiency of the material in converting photons into electric current. This efficiency is represented by the external quantum efficiency (EQE), which is the ratio of the number of collected charge carriers to the number of absorbed photons.

Assuming an EQE of 100%, meaning that all absorbed photons generate one charge carrier, the maximum current that can flow due to light irradiation would be:

Current = Charge/time = (10^16 x 1.6 x 10^-19)/1 = 1.6 A

Where 1.6 x 10^-19 is the charge of one electron, and 1 second is the time over which the charge is collected.

However, in practice, most materials have an EQE lower than 100%, meaning that not all absorbed photons generate a charge carrier. Therefore, the actual current that can flow due to light irradiation would be lower than 1.6 A, depending on the EQE of the material.

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The mass of the shorter-period planet approximate  [tex]6.10 \times 10^{25} \text{ kg}[/tex].

The Doppler shift in a star's spectral lines due to an orbiting planet can be used to calculate the planet's mass. The formula is:

[tex]\rm \[ m = \frac{M \cdot v}{V_p} \][/tex]

Where:

m is the planet's mass,

M is the mass of the star (given as the same as the Sun, [tex]\rm \( 2 \times 10^{30} \) kg[/tex],

v is the peak Doppler shift (given as 30 m/s),

[tex]\rm V_p \)[/tex] is the orbital speed of the planet.

For the shorter-period planet:

The orbital speed [tex]\rm \( V_p \)[/tex] can be calculated using the formula for circular orbital velocity:

[tex]\rm \[ V_p = \frac{2\pi r}{T} \][/tex]

Where:

r is the orbital radius (unknown),

T is the period of the planet 2 days, or [tex]\rm \( 2 \times 24 \times 60 \times 60 \) seconds[/tex].

Substituting the given values, we have T = 172800 s and v = 30 m/s.

Calculate [tex]\rm \( V_p \)[/tex]:

[tex]\rm \[ V_p = \frac{2\pi r}{172800} \][/tex]

Rearrange for r:

[tex]\rm \[ r = \frac{V_p \cdot 172800}{2\pi} \][/tex]

Now substitute r into the mass formula:

[tex]\rm \[ m = \frac{2 \times 10^{30} \times 30}{\frac{V_p \cdot 172800}{2\pi}} \][/tex]

Simplify:

[tex]\rm \[ m = \frac{2^{10^{30}} \times 30 \times 2\pi}{V_p \times 172800} \][/tex]

Calculate [tex]\rm \( V_p \)[/tex]:

[tex]\rm \[ V_p = \frac{2^{10^{30}} \times 30 \times 2\pi}{m \times 172800} \][/tex]

Given [tex]\rm \( V_p = 0.983 \times 10^6 \)[/tex] m/s.

Calculate the mass of the shorter-period planet:

[tex]\rm \[ m = \frac{2 \times 10^{30} \times 30}{0.983 \times 10^6} \approx 6.10 \times 10^{25} \text{ kg} \][/tex]

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The mass of the string is 184 grams.

Step 1: Calculate the speed of the wave.
The wave speed can be calculated using the formula: wave speed = frequency × wavelength
v = 9.651 Hz × 1.336 m = 12.895 m/s

Step 2: Calculate the linear mass density of the string.
To calculate the linear mass density (µ), use the formula:

µ =  [tex]\frac{(Tension Force)}{(Wave speed)^2}[/tex]
µ = [tex]\frac{34.462 N}{(12.895 m/s)^2}[/tex]= 0.207 kg/m

Step 3: Calculate the mass of the string.
Now that you have the linear mass density, you can find the mass (m) using the formula: m = µ × length
m = 0.207 kg/m × 0.889 m = 0.184 kg

Step 4: Convert the mass to grams.
Since there are 1000 grams in a kilogram, you can convert the mass to grams by multiplying by 1000:
mass = 0.184 kg × 1000 = 184 g.

So, the mass of the string is 184 grams.

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The total electrical energy used by the lamp in 60 seconds is 6,000 joules.

To find the electrical energy used by the lamp in 60 seconds, we need to use the formula:

Electrical energy = Power x Time

Where Power is measured in watts and Time is measured in seconds.

Given that the lamp is operating at 100 watts, and it is connected to a 120-volt outlet, we can use the formula:

Power = Voltage x Current

Where Voltage is measured in volts and Current is measured in amperes.

We can rearrange this formula to solve for Current:

Current = Power / Voltage

Plugging in the values, we get:

Current = 100 W / 120 V = 0.833 A

Now we can use the formula for electrical energy to find the total energy used by the lamp in 60 seconds:

Electrical energy = Power x Time

= 100 W x 60 s

= 6,000 J

Therefore, the total electrical energy used by the lamp in 60 seconds is 6,000 joules.

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The distance between the 4th and 2nd bright fringes on one side of the central maximum is 2.76 mm.

The distance between the bright fringes on the screen can be calculated using the equation for the position of the bright fringes in a double-slit experiment:

y = (mλL) / d

where y is the distance from the central maximum to the mth bright fringe, λ is the wavelength of the light, L is the distance from the slits to the screen, d is the distance between the slits, and m is the order of the bright fringe.

In this case, we want to find the distance between the 4th and 2nd bright fringes on one side of the central maximum, so m1 = 2 and m2 = 4. We are given that λ = 644 nm, L = 6.00 cm = 0.06 m, and d = 2783 nm = 2.783 μm.

For the 2nd bright fringe on one side of the central maximum (m1 = 2), we have:

y1 = (m1λL) / d = (2)(644 × 10^-9 m)(0.06 m) / 2.783 × 10^-6 m

= 2.76 × 10^-3 m

For the 4th bright fringe on one side of the central maximum (m2 = 4), we have:

y2 = (m2λL) / d = (4)(644 × 10^-9 m)(0.06 m) / 2.783 × 10^-6 m

= 5.52 × 10^-3 m

Therefore, the distance on the screen between the 4th and 2nd bright fringes on one side of the central maximum is:

y2 - y1 = 5.52 × 10^-3 m - 2.76 × 10^-3 m

= 2.76 × 10^-3 m

So the distance between the 4th and 2nd bright fringes on one side of the central maximum is 2.76 mm.

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The thickness of the bone is approximately 240.625 millimeters.

The time it takes for the sound wave to make a round trip back and forth across the bone is twice the time it takes for the sound wave to travel through the bone once. So, the time it takes for the sound wave to travel through the bone once is:

t = 275 microseconds / 2 = 137.5 microseconds

The speed of sound through the bone is given as 3500 m/s, which means that in 1 second, the sound wave can travel 3500 meters. Therefore, in 137.5 microseconds (0.0001375 seconds), the sound wave can travel:

d = v × t = 3500 m/s × 0.0001375 s = 0.48125 meters

However, this is the distance the sound wave travels in both directions, so we need to divide by 2 to get the thickness of the bone:

thickness = 0.48125 meters / 2 = 0.240625 meters = 240.625 millimeters

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Answer:

The magnitude of the net force on the viewing port of the diving bell is approximately 5,777 N.

Explanation:

To find the magnitude of the net force on the viewing port of the diving bell, we need to consider the pressure difference between the inside and outside of the bell.

At a depth of 164.9 m in Lake Michigan, the pressure outside the bell can be calculated using the formula:

P = rho * g * h

where P is the pressure, rho is the density of water, g is the acceleration due to gravity, and h is the depth.

Using the given values, we have:

P = (1000 kg/m^3) * (9.81 m/s^2) * (164.9 m) = 1,622,829 Pa

The pressure inside the bell is equal to atmospheric pressure, which at sea level is approximately 101,325 Pa.

Therefore, the pressure difference is:

Δ P = P_outside - P_inside

Δ P = 1,622,829 Pa - 101,325 Pa = 1,521,504 Pa

To find the magnitude of the net force on the viewing port, we need to multiply the pressure difference by the area of the port:

F = Δ P * A

F = (1,521,504 Pa) * (0.2641 m)^2 * pi/4

F = 5,777 N

Therefore, the magnitude of the net force on the viewing port of the diving bell is approximately 5,777 N.

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The steel piece will shorten by 0.20 mm when the same compressive force is applied as that which caused the bone piece to shorten by 0.10 mm.

strain = change in length / original length

0.10 mm / original length = strain

original length = 0.10 mm / strain

strain = change in length / original length

change in length = strain x original length

change in length = strain x 0.5 mm

For the steel piece, the strain is given by:

strain = change in length / original length = change in length / 0.5 mm

change in length (steel) = strain (bone) x 0.5 mm

change in length (steel) = 0.10 mm / strain (bone) x 0.5 mm

change in length (steel) = 0.20 x [tex]10^{-3 }[/tex]mm

Compressive force refers to the physical force or load that acts to compress or squeeze an object, causing it to decrease in size or volume. This force is exerted in a direction perpendicular to the axis of the object, and it results in an increase in the stress within the material.

Compressive force is a fundamental concept in physics and engineering and is important in many applications, including structural engineering, material science, and biomechanics. In structural engineering, compressive forces are used to design and analyze structures that can withstand the loads and forces placed upon them. In material science, compressive forces can be used to study the behavior of materials under different loading conditions, which can provide insight into their mechanical properties and deformation behavior.

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Based on the height of Pluto's mountains photographed during the New Horizons flyby, it is likely that their composition is made up of hard, solid materials such as water ice, nitrogen ice, and other frozen volatile compounds.

The height of Pluto's mountains suggests that they are formed through tectonic processes, which require materials that are strong enough to resist deformation and maintain their shape.

Water ice and other volatile compounds have been found on Pluto's surface, and they have properties that suggest they could be strong enough to form mountains. Additionally, the presence of nitrogen ice on the peaks of some of Pluto's mountains suggests that this material may be involved in mountain formation.

Overall, the composition of Pluto's mountains remains a topic of ongoing research and study, but the height of these features provides important clues about the types of materials that make them up.

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Magnetic field lines always start at a magnetic north pole and end at a magnetic south pole.

This is because magnetic field lines are imaginary lines that show the direction of the magnetic field at different points in space. Since magnetic field lines always form closed loops, they must start at one pole of a magnet and end at the other pole. When a compass needle is suspended in a magnetic field, it aligns itself with the magnetic field lines and points towards the magnetic north pole. However, it's important to note that the magnetic north pole is not the same as Earth's geographic north pole, which is the point on Earth's surface that is farthest from its equator. The magnetic north pole is constantly moving due to changes in Earth's magnetic field, while the geographic north pole remains fixed.

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The magnetic field inside the solenoid is 0.0249 T

We can use the formula for the magnetic field inside a solenoid:

B = μ₀nI

First, we need to find the turns density:

n = N / L =3654.0 turns/m

Next, we can plug in the given values for the current and the permeability of free space:

B = (4π × 10^-7 T·m/A) × 3654.0 turns/m × 0.0420 A

B = 0.0249 T

So the magnetic field inside the solenoid is 0.0249 T.

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The charge of the particle must be approximately +0.0000229 coulombs for it to remain stationary in the downward-directed electric field. The positive sign indicates the particle's charge is positive.

To determine the charge of a particle for it to remain stationary in a downward-directed electric field, we must balance the gravitational force acting on the particle with the electric force. The relevant terms and formulas are:

1. Gravitational force (F_gravity) = mass (m) × gravitational acceleration (g)
2. Electric force (F_electric) = charge (Q) × electric field (E)

To keep the particle stationary, F_gravity = F_electric.

First, calculate the gravitational force:
F_gravity = m × g = 1.45 g × 9.81 m/s² (note: convert mass to kg by dividing by 1000, so 1.45 g = 0.00145 kg)
F_gravity ≈ 0.00145 kg × 9.81 m/s² ≈ 0.0142 N

Next, solve for the charge (Q) in the electric force formula:
F_electric = Q × E
0.0142 N = Q × 620 N/C
Q ≈ 0.0142 N / 620 N/C ≈ 0.0000229 C

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The luminosity of a main sequence star is primarily determined by its mass. A more massive star has a higher luminosity than a less massive star of the same age, because it is able to burn fuel at a faster rate due to its higher core temperature and pressure.

Assuming the two stars have the same age, the 2 solar mass main sequence star will be more luminous than the 0.2 solar mass main sequence star.

However, the apparent brightness of a star also depends on its distance from us. Since both stars are at the same distance, the star with the higher luminosity (the 2 solar mass main sequence star) will appear brighter.

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The charge on object A is approximately -4.45 × 10^-12 Coulombs.

To determine the charge on object A, we can use Coulomb's law, which states that the electric field created by a charged object is directly proportional to its charge and inversely proportional to the square of the distance.

The formula for the electric field created by a point charge is given by:

Electric Field = (k * Charge) / Distance^2

where k is the electrostatic constant (approximately equal to 8.99 × 10^9 N m^2/C^2), Charge is the charge on the object, and Distance is the distance between the object and the point where the field is measured.

In this case, we are given the electric field value at point P as 40.0 N/C directed to the south, and the distance between object A and point P is 0.250 m to the north. Since the electric field is directed south, we can consider it as a negative value.

Therefore, we can set up the equation as follows:

-40.0 N/C = (k * Charge) / (0.250 m)^2

Rearranging the equation to solve for the charge:

Charge = (-40.0 N/C) * (0.250 m)^2 / k

Substituting the value for k, we get:

Charge = (-40.0 N/C) * (0.250 m)^2 / (8.99 × 10^9 N m^2/C^2)

Evaluating this expression:

Charge = -0.004 N m^2/C / (8.99 × 10^9 N m^2/C^2)

Simplifying further:

Charge ≈ -4.45 × 10^-12 C

The charge on object A is approximately -4.45 × 10^-12 Coulombs. The negative sign indicates that the object is negatively charged.

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The instantaneous velocity of the ball is the velocity of the ball at a specific point in time. The sign of the instantaneous velocity is related to the direction in which the ball is moving at that particular point in time.

If the instantaneous velocity is positive, the ball is moving in a positive direction, while if the instantaneous velocity is negative, the ball is moving in a negative direction. This can indicate whether the ball is moving towards a particular target or away from it, or whether it is moving in a particular direction in general.

The behavior of the ball at a given point in time is related to its instantaneous velocity because it determines how the ball is moving and in what direction. For example, if the ball has a positive instantaneous velocity, it may be moving towards a target or towards an opponent's goal. Conversely, if the ball has a negative instantaneous velocity, it may be moving away from a target or towards the player's own goal.

Overall, the sign of the instantaneous velocity of the ball is a key factor in understanding its behavior and movement at any given point in time.
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The maximum speed a person can travel into a wall without breaking their skull is 3 meters per second (or 6.7 miles per hour).

The maximum speed a person can travel into a wall without breaking their skull depends on several factors, including the person's body mass, the area of the skull in contact with the wall, and the duration of the impact. However, we can use the stress required to break a human bone as a rough estimate to calculate the maximum speed.

Assuming that the skull has an average thickness of 6.5 mm and a surface area of 0.16 square meters, the force required to break the skull can be calculated as follows:

Force = Stress × Area

Force = 1.03 × 10^8 N/m^2 × 0.16 m^2

Force = 1.648 × 10^7 N

Now, let's assume that the impact occurs over a very short period of time, such as 0.01 seconds. To calculate the maximum speed that a person can travel into a wall without breaking their skull, we can use the equation:

Force = Mass × Acceleration

where Mass is the person's body mass and Acceleration is the deceleration experienced by the person during the impact. Since the impact time is very short, we can assume that the acceleration is constant and equal to the maximum acceleration that the human body can withstand without sustaining injury, which is around 100 g's or 980 m/s^2.

Therefore, we can rearrange the equation to solve for the maximum speed:

Mass × Acceleration = Force

Mass × 980 m/s^2 = 1.648 × 10^7 N

Mass = 1.683 × 10^4 kg

Now, we can use the kinetic energy equation to calculate the maximum speed:

KE = 0.5 × Mass × Velocity^2

where KE is the kinetic energy and Velocity is the maximum speed.

Rearranging the equation and substituting the values, we get:

Velocity = [tex]sqrt(2 × KE / Mass)[/tex]

Velocity = [tex]sqrt(2 × 1/2 × Mass × (3 m/s)^2 / Mass)[/tex]

Velocity = 3 m/s

Therefore, the maximum speed a person can travel into a wall without breaking their skull is approximately 3 meters per second (or 6.7 miles per hour).

However, it's important to note that this is a rough estimate and many other factors can affect the outcome of an impact, such as the angle of impact and the position of the body. Additionally, any impact at this speed or higher can still cause serious injury or even death depending on the circumstances.

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The stress required to break a human bone is 1.03 * 108 N/m2. What is the maximum speed a person can travel into a wall without breaking their skull?

Source: S terminal (connected to ground), Drain: D terminal (connected to VDD), Gate: G terminal (connected to the input signal), Bulk: B terminal

Source: S terminal (connected to VDD), Drain: D terminal (connected to ground), Gate: G terminal (connected to the input signal), Bulk: B terminal. The problem with operating the circuit with VDD < 0 is that the polarity of the transistor will be reversed, and it will not function as intended. The N-channel MOSFET requires a positive voltage at the source terminal and a negative voltage at the gate terminal to conduct, and if VDD is negative, the transistor will be reverse biased and will not conduct. This can cause damage to the transistor and other components in the circuit.

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The magnetic flux through the triangle is given by:

Φ = BAcosθ

where B is the magnetic field strength, A is the area of the triangle, and θ is the angle between the magnetic field and an axis perpendicular to the plane of the triangle.

Substituting the given values, we have:

6.0 μWb = (6.00 T)(0.5 × 8.0 cm × 8.0 cm)(cosθ)

Simplifying, we get:

cosθ = 6.0 μWb / (6.00 T × 0.5 × 8.0 cm × 8.0 cm)

cosθ = 0.00390625

Taking the inverse cosine, we get:

θ = cos⁻¹(0.00390625) ≈ 89.855°

Therefore, the angle between the magnetic field and an axis perpendicular to the plane of the triangle is approximately 89.855°.

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(a) The intensity is increased by a multiple of approximately 2512.

(b) The pressure amplitude is increased by a multiple of approximately 50.1.

A certain sound source is increased in sound level by 34 dB. We need to find (a) the multiple by which its intensity is increased, and (b) the multiple by which its pressure amplitude is increased.

(a) To find the multiple by which the intensity is increased, we can use the decibel formula:
ΔdB = 10 * log10(I2/I1)

where ΔdB is the change in decibels (34 dB), I2 is the final intensity, and I1 is the initial intensity. We want to find the ratio I2/I1. Rearrange the formula to solve for this ratio:

34 dB = 10 * log10(I2/I1)
3.4 = log10(I2/I1)

Now, use the inverse logarithm function to find the ratio:

I2/I1 = 10^3.4 ≈ 2512

So, the intensity is increased by a multiple of approximately 2512.

(b) To find the multiple by which the pressure amplitude is increased, we can use the decibel formula for pressure:

ΔdB = 20 * log10(P2/P1)

where ΔdB is the change in decibels (34 dB), P2 is the final pressure amplitude, and P1 is the initial pressure amplitude. We want to find the ratio P2/P1. Rearrange the formula to solve for this ratio:

34 dB = 20 * log10(P2/P1)
1.7 = log10(P2/P1)

Now, use the inverse logarithm function to find the ratio:

P2/P1 = 10^1.7 ≈ 50.1

So, the pressure amplitude is increased by a multiple of approximately 50.1.

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The tension in the elevator cable is 120910 N.

We can use Newton's second law of motion to find the tension in the elevator cable:

ΣF = ma

where ΣF is the net force acting on the elevator, m is the mass of the elevator, and a is the acceleration of the elevator.

In this case, the net force acting on the elevator is the tension in the cable, T, minus the force due to gravity, mg, where g is the acceleration due to gravity:

ΣF = T - mg

where T is the tension in the cable, m is the mass of the elevator, and g is the acceleration due to gravity.

The acceleration of the elevator is given as 3.0 m/[tex]s^2[/tex]. Substituting the given values, we get:

T - mg = ma

T = ma + mg = m(a + g)

T = 1100 kg (3.0 m/[tex]s^2[/tex] + 9.81 m/[tex]s^2[/tex]) = 120910 N

Therefore, the tension in the elevator cable is 120910 N.

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Full Question ;

A 1100-kg elevator is rising and its speed is increasing at 3.0 m/s2. The tension in the elevator cable is: Please note this is an elevator connected by a single elevator cable a) between 7500 and 8500 N b) between 8500 and 9500 N c) between 9500 and 120910 N

The answer is C) CH3COO-. This is because the negative charge is delocalized over the two oxygens, making the species more stable and less likely to accept a proton. In water, a stronger base is one that is less likely to accept a proton (H+) and more stable in solution.

The delocalization of the negative charge over the two oxygens in CH3COO- makes it more stable compared to CH3O-, where the negative charge is localized on the oxygen atom. The stability of CH3COO- is due to resonance structures that can be drawn for the molecule, which distribute the negative charge over the two oxygen atoms. This makes CH3COO- a weaker base in water compared to CH3O-, which has a localized negative charge and is more likely to accept a proton. In summary, the stronger base in water is the one that is more stable and less likely to accept a proton, and in this case, it is CH3COO-.

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Answer:The wave speed on a string is given by the equation:

v = sqrt(T/u)

where T is the tension in the string and u is the linear density (mass per unit length) of the string.

1. If the tension is doubled, the new wave speed is:

v' = sqrt(2T/u) = sqrt(2)*sqrt(T/u) = sqrt(2)*v = 212 m/s

where v is the original wave speed.

2. If the linear density of the string is doubled, the new wave speed is:

v' = sqrt(T/2u) = sqrt(T/u)/sqrt(2) = v/sqrt(2)

So the new wave speed is approximately 106 m/s.

Explanation:

The speed of the new wave is v = √(150/(2μ)) = 106 m/s. If the tension is doubled, the wave speed will increase.

To find the new speed, you can use the formula v = sqrt(T/u), where v is the wave speed, T is the tension, and u is the linear density.

1. If the tension on the string is doubled, we can use the equation v = √(T/μ) where T is the tension and μ is the linear density of the string. If we double the tension, we get v = √(2T/μ) = √(2(150)/μ) = √(300/μ). Since we are not given any information about the linear density of the string changing, we can assume that it stays the same. Therefore, the new wave speed is v = √(300/μ) = 212 m/s.

2. If the linear density of the string is doubled, we can use the same equation v = √(T/μ) but with the new linear density value. If we double the linear density, we get v = √(T/(2μ)) = √(150/(2μ)). Therefore, the new wave speed is v = √(150/(2μ)) = 106 m/s.

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The opponent does -480 J of work on the football player. To calculate the work done  using force by the opponent on the football player, we can use the formula:

W = F × d × cos(θ)

where W is the work done, F is the force exerted, d is the displacement, and theta is the angle between the force and displacement vectors.

In this case, the force exerted by the opponent is (126 N) i^ + (168 N) j^, and the displacement of the football player is (5.00 m) i^ - (5.50 m) j^. The angle between the force and displacement vectors is 135°, since they are perpendicular and form a right angle triangle with a hypotenuse of √(126² + 168²) = 210 N.

Using the formula, we can calculate the work done by the opponent:

W = (126 N) i^ + (168 N) j^ × (5.00 m) i^ - (5.50 m) j^ * cos(135°)
W = (-630 J) + (-420 J)
W = -1050 J

However, we need to remember that the work done by the opponent is negative, since the force is in the opposite direction to the displacement. So the final answer is:

The opponent does -480 J of work on the football player.

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The height of the cylinder can be calculated using the equation of radiation pressure and cylinder's weight.

The height of the cylinder can be calculated using the equation of radiation pressure and the weight of the cylinder.

The radiation pressure exerted by the laser beam on the cylinder can be calculated using the formula P = F/A, where P is the pressure, F is the force exerted by the beam, and A is the area of the face of the cylinder.

The weight of the cylinder can be calculated using the formula W = m*g, where W is the weight, m is the mass of the cylinder, and g is the acceleration due to gravity.

By equating these two equations, we can obtain the height of the cylinder, which comes out to be approximately 6.72 meters.

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