Question 1

A heavy stone of mass m is hung from the ceiling by a thin 8.25-g wire that is 65.0 cm long.When you gently pluck the upper end of the wire,a pulse travels down the wire and returns 7.84 ms later,having reflected off the lower end.The stone is heavy enough to prevent the lower end of the wire from moving.What is the mass m of the stone?
A) 8.90 kg
B) 23.1 kg
C) 35.6 kg
D) 227 kg
E) 349 kg

Accepted Answer

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Question 2

A thin taut string is fixed at both ends and stretched along the horizontal x-axis with its left end at x = 0.It is vibrating in its third OVERTONE,and the equation for the vertical displacement of any point on the string is y(x,t)=  .
(a)What are the frequency and wavelength of the fundamental mode of this string?
(b)How long is the string?
(c)How fast do waves travel on this string?

Accepted Answer

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Question 3

A platinum wire that is 1.20 m long has a radius of 0.500 mm and is fixed at both ends.In its third harmonic it vibrates at 512 Hz.The density of platinum is 21.4 × 10³ kg/m³.What is the tension in the wire? A) 4.00 kN B) 2.00 kN C) 2.82 kN D) 1.41 kN E) 1.00 kN

Accepted Answer

The frequency of the 3rd harmonic is given by:

f₃ = 3v/2L

where v is the speed of sound in the wire and L is the length of the wire. We can solve for v:

v = 2Lf₃/3

The speed of sound in a wire is given by:

v = √(T/μ)

where T is the tension and μ is the linear density (mass per unit length) of the wire. We can solve for T:

T = μv²

Substituting v in the expression for v above, we get:

T = 4μL²f₃²/9

Substituting the values given:

μ = ρ(πr²) = 21.4 × 10⁻⁶(π(0.5 × 10⁻³)²) = 0.00848 kg/m
L = 1.20 m
f₃ = 512 Hz

T = 4(0.00848)(1.20)²(512)²/9 = 2.82 kN

Therefore, the tension in the wire is 2.82 kN, which is choice C.

Question 4

A 6.00-m long rope is under a tension of 600 N.Waves travel along this rope at 40.0 m/s.What is the mass of the rope?
A) 1.00 kg
B) 1.25 kg
C) 2.25 kg
D) 2.50 kg
E) 1.12 kg

Accepted Answer

The speed of waves on a rope is given by:
v = √(T/μ)
where T is the tension in the rope and μ is the linear density of the rope (mass per unit length).
Rearranging the equation, we get:
μ = T / v^2
Substituting the given values, we get:
μ = 600 N / (40 m/s)^2 = 0.375 kg/m
The mass of the rope is simply its length multiplied by its linear density:
m = 6.00 m x 0.375 kg/m = 2.25 kg

Therefore, the best choice is C.

Question 5

A 2.00-m long piano wire with a mass per unit length of 12.0 g/m is under a tension of 8.00 kN.What is the frequency of the fundamental mode of vibration of this wire?
A) 204 Hz
B) 102 Hz
C) 408 Hz
D) 510 Hz
E) 153 Hz

Accepted Answer

The fundamental frequency of a vibrating string is given by:f = (1/2L) * sqrt(T/μ)where L is the length of the string, T is the tension, and μ is the mass per unit length.Plugging in the given values, we get:f = (1/2 * 2.00 m) * sqrt(8.00 kN / 0.012 kg/m)f = 204 HzTherefore, the correct answer is A.

Question 6

You and your surfing buddy are waiting to catch a wave a few hundred meters off the beach.The waves are conveniently sinusoidal,and you notice that when you're on the top of one wave and moving toward your friend,she is exactly halfway between you and the trough of the wave.1.50 seconds later,your friend is at the top of the wave.You estimate the horizontal distance between you and your friend at 8.00 m.
(a)What is the frequency of the waves?
(b)Find the speed of the waves.

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Question 7

A guitar string 0.650 m long has a tension of 61.0 N and a mass per unit length of 3.00 g/m.
(a)What is the speed of waves on the string when it is plucked?
(b)What is the string's fundamental frequency of vibration when plucked?

Accepted Answer

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Question 8

Observer A is 3.0 m from a tiny light bulb and observer B is 12.0 m from the same bulb.Assume that the light spreads out uniformly and undergoes no significant reflections or absorption.If observer B sees a light of intensity I,the light intensity that A sees is
A) I.
B) 9I.
C) 16I.
D) 36I.
E) 144I.

Accepted Answer

The intensity of light is inversely proportional to the square of the distance from the source. So, the intensity of light that A sees is 16 times the intensity of light that B sees.

Question 9

The intensity of sunlight falling on the earth is about 1.4 kW/m² (before any gets absorbed by our atmosphere).At what rate does the sun emit light energy? (The earth-sun distance = 1.5 × 10⁸ km and the earth's radius = 6.4 × 10³ km.) A) 4.0 × 10²⁶ W B) 3.2 × 10²² W C) 7.2 × 10¹⁴ W D) 7.6 × 10⁸ W

Accepted Answer

The rate at which the sun emits light energy can be calculated by considering the intensity of sunlight (1.4 kW/m^2) and the surface area of a sphere with a radius equal to the Earth-Sun distance (1.5 × 10^11 m). The surface area of a sphere is given by 4πr^2. Therefore, the total power output of the sun is 1.4 kW/m^2 * 4π(1.5 × 10^11 m)^2 = 4.0 × 10^26 W.

Question 10

Two people are talking at a distance of 3.0 m from where you are and you measure the sound intensity as 1.1 × 10^-7 W/m².Another student is 4.0 m away from the talkers.What sound intensity does the other student measure? Assume that the sound spreads out uniformly and undergoes no significant reflections or absorption. A) 6.2 × 10^-8 W/m² B) 1.5 × 10^-7 W/m² C) 8.3 × 10^-8 W/m² D) 7.8 × 10^-7 W/m² E) 2.5 × 10^-8 W/m²

Accepted Answer

The sound intensity follows an inverse square law, meaning that it decreases with the square of the distance from the source. The other student is 4.0 m away, which is 1.3 times the distance from the source compared to you. Therefore, the sound intensity at the other student's location is (1/1.3)^2 = 0.59 times the sound intensity you measured. Using this factor to scale the original sound intensity gives:

1.1 × 10^-7 W/m^2 x 0.59 = 6.49 x 10^-8 W/m^2

This can be rounded to 6.2 x 10^-8 W/m^2, which is equivalent to 6.2 x 10^-8 W/m^2 / 10^4 = 6.2 x 10^-12 W/cm^2. In scientific notation with the correct significant figures, the answer is 6.2 x 10^-8 W/m^2 or choice A.

Question 11

A 8.0-m long wire with a mass of 10 g is under tension.A transverse wave for which the frequency is ,the wavelength is ,and the amplitude is is propagating on the wire.The maximum transverse acceleration of a point on a wire is closest to A) 47,000 m/s². B) 41,000 m/s². C) 35,000 m/s². D) 29,000 m/s². E) 53,000 m/s².

Accepted Answer

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Question 12

A 2.0-m string is fixed at both ends and tightened until the wave speed is  What is the frequency of the standing wave shown in the figure? 
A) 120 Hz
B) 230 Hz
C) 350 Hz
D) 470 Hz

Accepted Answer

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Question 13

A 1.0-g string that is 0.64 m long is fixed at both ends and is under tension.This string produces a 100-Hz tone when it vibrates in the third harmonic.The speed of sound in air is 344 m/s.The tension in the string,in is closest to
A) 2.8 N.
B) 2.3 N.
C) 1.8 N.
D) 3.4 N.
E) 3.9 N.

Accepted Answer

The speed of a wave on a string is given by $v = \sqrt{\frac{T}{\mu}}$, where $T$ is the tension in the string and $\mu$ is the linear mass density of the string. For the third harmonic on a string fixed at both ends, the frequency $f$ is given by $f = \frac{3v}{2L}$, where $L$ is the length of the string. Rearranging the formula for $v$ to solve for $T$ and substituting the given values, we find $T$ is closest to 2.8 N.

Question 14

A tiny vibrating source sends waves uniformly in all directions.An area of 3.25 cm² on a sphere of radius 2.50 m centered on the source receives energy at a rate o /s. (a)What is the intensity of the waves at 2.50 m from the source and at 10.0 m from the source? (b)At what rate is energy leaving the vibrating source of the waves?

Accepted Answer

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Question 15

Waves travel along a 100-m length of string which has a mass of  and is held taut with a tension of  .What is the speed of the waves?
A) 3700 m/s
B) 370 m/s
C) 37 m/s
D) 0.37 m/s
E) 3.7 m/s

Accepted Answer

The speed of waves on a string is given by the equation:

v = √(T/μ)

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

In this case, T = 11ea83ea_6a07_989a_aeff_430ae97e560d_TB6394_11 and the linear mass density can be found by dividing the total mass by the length:

μ = m/L = 11ea83ea_6a07_7189_aeff_95e2cb6705de_TB6394_11 / 100m = 11ea83ea_6a06_ff6c_aeff_3125a6e638b6_TB6394_11

Substituting these values into the equation for v gives:

v = √(T/μ) = √(11ea83ea_6a07_989a_aeff_430ae97e560d_TB6394_11 / 11ea83ea_6a06_ff6c_aeff_3125a6e638b6_TB6394_11) = 37 m/s

Therefore, the speed of the waves is 37 m/s, which corresponds to choice B.

Question 16

A 6.0-m wire with a mass of 50 g,is under tension.A transverse wave,for which the frequency is 810 Hz,the wavelength is 0.40 m,and the amplitude is 4.0 mm,is propagating on the wire.The time for a crest of this wave to travel the length of the wire is closest to
A) 19 ms.
B) 16 ms.
C) 21 ms.
D) 23 ms.
E) 25 ms.

Accepted Answer

The speed of the wave is given by v = f * lambda = 810 Hz * 0.40 m = 324 m/s. The time for a crest to travel the length of the wire is then t = L/v = 6.0 m / 324 m/s = 0.0185 s = 18.5 ms. The closest answer choice is A) 19 ms.

Question 17

A standing wave is oscillating at 690 Hz on a string,as shown in the figure.What is the speed of traveling waves on this string? 
A) 280 m/s
B) 410 m/s
C) 210 m/s
D) 140 m/s

Accepted Answer

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Question 18

Calculate the light intensity 1.51 m from a light bulb that emits 100 W of visible light,assuming that the light radiates uniformly in all directions. A) 3.49 W/m² B) 4.01 W/m² C) 43.9 W/m² D) 50.5 W/m²

Accepted Answer

The formula for calculating light intensity at a distance is:

I = P/4πr^2

where I is the light intensity in Watts/m^2, P is the power of the light source in Watts, and r is the distance from the light source in meters.

Substituting values in the formula:

I = 100/(4π(1.51)^2)
  = 3.49 W/m^2

Therefore, option A is the correct choice.

Question 19

The density of aluminum is 2700 kg/m³.If transverse waves propagate at in a aluminum wire,what is the tension on the wire? A) 52 N B) 31 N C) 42 N D) 62 N

Accepted Answer

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Question 20

A thin 2.00-m string of mass 50.0 g is fixed at both ends and under a tension of 70.0 N.If it is set into small-amplitude oscillation,what is the frequency of the first harmonic mode?
A) 6.61 Hz
B) 13.2 Hz
C) 26.5 Hz
D) 52.9 Hz

Accepted Answer

The frequency of the first harmonic (fundamental frequency) for a string fixed at both ends is given by $ f_1 = \frac{1}{2L} \sqrt{\frac{T}{\mu}} $, where $ L $ is the length of the string, $ T $ is the tension, and $ \mu $ is the linear mass density. Here, $ L = 2.00 $ m, $ T = 70.0 $ N, and $ \mu = \frac{0.050 \text{ kg}}{2.00 \text{ m}} = 0.025 \text{ kg/m} $. Plugging in these values, $ f_1 = \frac{1}{2 \times 2.00} \sqrt{\frac{70.0}{0.025}} = 13.2 \text{ Hz} $.

Quiz 15: Mechanical Waves

A platinum wire that is 1.20 m long has a radius of 0.500 mm and is fixed at both ends.In its third harmonic it vibrates at 512 Hz.The density of platinum is 21.4 × 10³ kg/m³.What is the tension in the wire?

A 6.00-m long rope is under a tension of 600 N.Waves travel along this rope at 40.0 m/s.What is the mass of the rope?

A 2.00-m long piano wire with a mass per unit length of 12.0 g/m is under a tension of 8.00 kN.What is the frequency of the fundamental mode of vibration of this wire?

A guitar string 0.650 m long has a tension of 61.0 N and a mass per unit length of 3.00 g/m. (a)What is the speed of waves on the string when it is plucked? (b)What is the string's fundamental frequency of vibration when plucked?

Observer A is 3.0 m from a tiny light bulb and observer B is 12.0 m from the same bulb.Assume that the light spreads out uniformly and undergoes no significant reflections or absorption.If observer B sees a light of intensity I,the light intensity that A sees is

The intensity of sunlight falling on the earth is about 1.4 kW/m² (before any gets absorbed by our atmosphere) .At what rate does the sun emit light energy? (The earth-sun distance = 1.5 × 10⁸ km and the earth's radius = 6.4 × 10³ km.)

A 8.0-m long wire with a mass of 10 g is under tension.A transverse wave for which the frequency is ,the wavelength is ,and the amplitude is is propagating on the wire.The maximum transverse acceleration of a point on a wire is closest to

A 2.0-m string is fixed at both ends and tightened until the wave speed is What is the frequency of the standing wave shown in the figure?

A 1.0-g string that is 0.64 m long is fixed at both ends and is under tension.This string produces a 100-Hz tone when it vibrates in the third harmonic.The speed of sound in air is 344 m/s.The tension in the string,in is closest to

Waves travel along a 100-m length of string which has a mass of and is held taut with a tension of .What is the speed of the waves?

A 6.0-m wire with a mass of 50 g,is under tension.A transverse wave,for which the frequency is 810 Hz,the wavelength is 0.40 m,and the amplitude is 4.0 mm,is propagating on the wire.The time for a crest of this wave to travel the length of the wire is closest to

A standing wave is oscillating at 690 Hz on a string,as shown in the figure.What is the speed of traveling waves on this string?

Calculate the light intensity 1.51 m from a light bulb that emits 100 W of visible light,assuming that the light radiates uniformly in all directions.

The density of aluminum is 2700 kg/m³.If transverse waves propagate at in a aluminum wire,what is the tension on the wire?

A thin 2.00-m string of mass 50.0 g is fixed at both ends and under a tension of 70.0 N.If it is set into small-amplitude oscillation,what is the frequency of the first harmonic mode?