Question 1

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 2

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 sun emits energy uniformly in all directions. The intensity at the Earth's distance is 1.4 kW/m². The surface area of a sphere with a radius equal to the Earth-Sun distance is 4π(1.5 × 10^11 m)². Multiplying the intensity by this area gives the total power output of the sun, which is approximately 4.0 × 10^26 W.

Question 3

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

The answer of A standing wave is oscillating at 690...

Question 4

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 answer of Observer A is 3.0 m from a...

Question 5

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 answer of A thin 2.00-m string of mass 50.0...

Question 6

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

The answer of A guitar string 0.650 m long has...

Question 7

A tiny vibrating source sends waves uniformly in all directions. An area of 3.25 cm²on a sphere of radius 2.50 m centered on the source receives energy at a rate of 4.20 J/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

The answer of A tiny vibrating source sends waves uniformly...

Question 8

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

The answer of A heavy stone of mass m is...

Question 9

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.

Accepted Answer

The answer of You and your surfing buddy are waiting...

Question 10

A 8.0-m long wire with a mass of 10 g is under tension. A transverse wave for which the frequency is 570 Hz, the wavelength is 0.10 m, and the amplitude is 3.7 mm 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

The maximum transverse acceleration of a point on a wire is given by:$$a_{max} = \omega^2 A$$where $\omega$ is the angular frequency and $A$ is the amplitude.The angular frequency is given by:$$\omega = 2\pi f$$where $f$ is the frequency.Substituting the given values into these equations, we get:$$\omega = 2\pi (570 ext{ Hz}) = 3570 ext{ rad/s}$$$$a_{max} = (3570 ext{ rad/s})^2 (0.0037 ext{ m}) = 47,000 ext{ m/s}^2$$Therefore, the maximum transverse acceleration of a point on the wire is closest to 47,000 m/s².

Question 11

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 third harmonic is given by:
f = (3v)/(2L)
where v is the speed of sound in the wire and L is its length.
Rearranging, we have:
v = (2Lf)/3
The speed of sound in a wire is given by:
v = sqrt(T/µ)
where T is the tension in the wire and µ is its linear density (mass per unit length).
Rearranging, we have:
T = µv^2
Substituting the expressions for v and µ, we get:
T = (4L^2f^2µ)/9
Substituting the given values, we get:
T = (4 x (1.20 m)^2 x (512 Hz)^2 x 21.4 x 10^3 kg/m) / 9
T = 2820 N = 2.82 kN (to three significant figures)
Therefore, the best choice is C, which gives the correct tension in the wire.

Question 12

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 under tension is given by v = sqrt(T/μ), where T is the tension and μ is the linear density (mass per unit length) of the rope. Rearranging to solve for μ, we get μ = T/v^2. Plugging in the given values, we get:
μ = 600 N / (40.0 m/s)^2 = 0.375 kg/m
To find the mass of the rope, we multiply μ by the length L: m = μL = 0.375 kg/m * 6.00 m = 2.25 kg. Therefore, the answer is C.

Question 13

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 intensity of sound decreases with the square of the distance from the source. So, the intensity at 4.0 m is (3.0 m/4.0 m)^2 * 1.1 × 10^-7 W/m^2 = 6.2 × 10^-8 W/m^2.

Question 14

A 2.0-m string is fixed at both ends and tightened until the wave speed is 78m/s. 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

The answer of A 2.0-m string is fixed at both...

Question 15

The density of aluminum is 2700 kg/m3. If transverse waves propagate at 34 m/s in a 4.6-mm diameter aluminum wire, what is the tension on the wire?
A) 52 N
B) 31 N
C) 42 N
D) 62 N

Accepted Answer

The tension in the wire can be calculated using the formula for the speed of transverse waves: v = sqrt(T/μ), where μ is the linear mass density (mass per unit length). First, calculate μ using the density and cross-sectional area of the wire, then solve for T using the given wave speed.

Question 16

Waves travel along a 100-m length of string which has a mass of 55 g and is held taut with a tension of 75 N. 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 answer of Waves travel along a 100-m length of...

Question 17

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 answer of A 2.00-m long piano wire with a...

Question 18

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) = (1.22 cm) sin[(14.4 m^-1)x] cos[(166 rad/s)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

The answer of A thin taut string is fixed at...

Question 19

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 answer of A 6.0-m wire with a mass of...

Question 20

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 intensity of light is calculated using the formula I = P / (4πr²), where P is the power (100 W) and r is the distance (1.51 m). Substituting the values, I = 100 / (4π(1.51)²) ≈ 3.49 W/m².

Quiz 14: Mechanical Waves

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

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 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?

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 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 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?

A 8.0-m long wire with a mass of 10 g is under tension. A transverse wave for which the frequency is 570 Hz, the wavelength is 0.10 m, and the amplitude is 3.7 mm is propagating on the wire. The maximum transverse acceleration of a point on a wire is closest to

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 2.0-m string is fixed at both ends and tightened until the wave speed is 78m/s. What is the frequency of the standing wave shown in the figure?

The density of aluminum is 2700 kg/m3. If transverse waves propagate at 34 m/s in a 4.6-mm diameter aluminum wire, what is the tension on the wire?

Waves travel along a 100-m length of string which has a mass of 55 g and is held taut with a tension of 75 N. What is the speed of the waves?

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 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

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.