Question 1

Which of the following seismic waves travels the slowest?
A) surface waves
B) pressure waves
C) shear waves
D) both surface and pressure waves

Accepted Answer

Surface waves travel the slowest among seismic waves, as they move along the Earth's surface and have lower velocities compared to pressure (P) and shear (S) waves.

Question 2

A 100-m long high-voltage cable is suspended between two towers. The mass of the 100-m cable is 200 kg. If the tension in the cable is 20,000 N, what is the lowest frequency at which this cable can oscillate?
A) 0.50 Hz
B) 0.61 Hz
C) 0.75 Hz
D) 1.5 Hz

Accepted Answer

The answer of A 100-m long high-voltage cable is suspended...

Question 3

A 1.5-m string is held fixed at both ends. When driven by a 180-Hz source, the string vibrates in 3 distinct segments. What is the natural fundamental frequency of the string?
A) 30 Hz
B) 60 Hz
C) 90 Hz
D) 540 Hz

Accepted Answer

The length of the string is divided into 3 segments, so each segment has a length of 0.5 m. The fundamental frequency of a string is given by f = (1/2L)√(T/μ), where L is the length of the string, T is tension in the string, and μ is the linear density of the string. Since the length and linear density of the string are constant, the only factor affecting the fundamental frequency is tension. The frequency of the driving source does not determine the fundamental frequency. Therefore, the natural fundamental frequency of the string is f = (1/2*0.5)√(T/μ) = √(T/μ), which is independent of the driving frequency. None of the given choices match the calculated frequency, so the answer is not listed.

Question 4

Tripling the tension in a guitar string will change its natural frequency by what factor? A) 3 B) 3^1/2 C) 3^-1/2 D) 1.5

Accepted Answer

The answer of Tripling the tension in a guitar string...

Question 5

A C note (f = 128 Hz) is sounded on a piano. If the length of the piano wire is 1.00 m and its mass density is 5.00 g/m, what is the tension in the wire?
A) 84 N
B) 328 N
C) 655 N
D) 1310 N

Accepted Answer

The frequency (f) of a string vibrating in its fundamental mode is given by:

f = (1/2L)√(T/μ),

where L is the length of the string, T is the tension in the string, and μ is the mass per unit length of the string.

Rearranging the formula, we can solve for T:

T = (4L^2μf^2)

Plugging in the values given:

T = (4*1.00^2*5.00*10^-3*(128)^2)
T = 328 N

Question 6

An earthquake emits both P waves and S waves that travel at different speeds through the Earth. Suppose a P wave travels at 8000 m/s and an S wave at 4000 m/s. If P waves are received at a seismic station 20.0 s before an S wave arrives, how far is the station from the earthquake center?
A) 80 km
B) 160 km
C) 240 km
D) 320 km

Accepted Answer

The answer of An earthquake emits both P waves and...

Question 7

If a guitar string has a fundamental frequency of 250 Hz, what is the frequency of its third harmonic?
A) 250 Hz
B) 750 Hz
C) 1000 Hz
D) 1500 Hz

Accepted Answer

The answer of If a guitar string has a fundamental...

Question 8

Are the P waves and the S waves associated with earthquakes transverse or longitudinal?
A) Both are transverse.
B) Both are longitudinal.
C) P waves are transverse, and S waves are longitudinal.
D) P waves are longitudinal, and S waves are transverse.

Accepted Answer

P waves are longitudinal waves, meaning they compress and expand the material they move through. S waves are transverse waves, meaning they move the ground up and down or side-to-side perpendicular to the direction of wave travel.

Question 9

A string of length L with fixed ends is made to go into standing wave patterns. What is the longest wavelength associated with all possible standing wave patterns in this situation?
A) L/4
B) L/2
C) L
D) 2L

Accepted Answer

The answer of A string of length L with fixed...

Question 10

If the tension on a guitar string is increased by a factor of 2, the fundamental frequency at which it vibrates is changed by what factor? A) 0.5 B) 2^1/2 C) 2^-1/2 D) 2

Accepted Answer

The answer of If the tension on a guitar string...

Question 11

A standing wave is set up in a 100-cm string fixed at both ends. The string vibrates in 5 distinct segments when driven by a 120-Hz source. What is the wavelength?
A) 10 cm
B) 20 cm
C) 40 cm
D) 80 cm

Accepted Answer

The number of segments that vibrate in a standing wave is equal to the number of half wavelengths in the string. Therefore, if the string vibrates in 5 segments, there must be 5 half wavelengths in the string. Since the length of the string is 100 cm, each half wavelength is 100 cm / 5 = 20 cm. Therefore, the wavelength of the standing wave is twice the half wavelength, or 2 x 20 cm = 40 cm. So, the correct answer is C) 40 cm.

Question 12

A string with fixed ends is made to go into standing wave patterns. At a given tension, the lowest frequency for which such a pattern exists is 150 Hz. Which of the following frequencies would also cause a standing wave pattern in this case?
A) 250 Hz
B) 500 Hz
C) 750 Hz
D) All of the above frequencies will cause a standing wave pattern in this case.

Accepted Answer

The answer of A string with fixed ends is made...

Question 13

How many nodes does a standing wave in a string have at the frequency of the sixth harmonic?
A) 12
B) 6
C) 3
D) The answer is not given.

Accepted Answer

The answer of How many nodes does a standing wave...

Question 14

If I double the mass per unit length of guitar string, its natural frequency changes by what factor?
A) 2.0
B) 1.4
C) 1.0
D) 0.71

Accepted Answer

The natural frequency of a guitar string is proportional to the square root of its tension divided by its linear density (mass per unit length). When the mass per unit length is doubled, the tension must also be doubled in order for the string to stay in tune. However, this only results in a √2 = 1.4-fold increase in frequency. Therefore, the natural frequency changes by a factor of 0.71 (1/1.4) when the mass per unit length is doubled.

Question 15

For a standing wave on a string, the wavelength must equal:
A) the distance between adjacent nodes.
B) the distance between adjacent antinodes.
C) twice the distance between adjacent nodes.
D) the distance between supports.

Accepted Answer

The wavelength of a standing wave on a string is twice the distance between adjacent nodes because one complete wavelength includes a node, an antinode, another node, and back to the first node, which is twice the node-to-node distance.

Question 16

The lowest A on a piano has a frequency of 27.5 Hz. If the tension in the 2.0-m long string is 151 N and one-half wavelength occupies the string, what is the mass of the string?
A) 100 g
B) 25 g
C) 37 g
D) 50 g

Accepted Answer

The answer of The lowest A on a piano has...

Question 17

I stretch a rubber band and "plunk" it to make it vibrate in its fundamental frequency. I then stretch it to twice its length and make it vibrate in the fundamental frequency once again. This rubber band is made so that doubling its length doubles the tension and reduces the mass per unit length by a factor of 2. The new frequency will be related to the old by a factor of:
A) 4.0.
B) 2.0.
C) 1.4.
D) 1.0.

Accepted Answer

The answer of I stretch a rubber band and "plunk"...

Question 18

A standing wave is set up in a 2.0-m string fixed at both ends. The string vibrates in 3 distinct segments when driven by a 120-Hz source. In how many distinct standing wave segments will the string vibrate if the tension is increased by a factor of 4?
A) 3
B) 6
C) 9
D) No standing wave pattern occurs.

Accepted Answer

The answer of A standing wave is set up in...

Quiz 12: Waves

Which of the following seismic waves travels the slowest?

A 100-m long high-voltage cable is suspended between two towers. The mass of the 100-m cable is 200 kg. If the tension in the cable is 20,000 N, what is the lowest frequency at which this cable can oscillate?

A 1.5-m string is held fixed at both ends. When driven by a 180-Hz source, the string vibrates in 3 distinct segments. What is the natural fundamental frequency of the string?

Tripling the tension in a guitar string will change its natural frequency by what factor?

A C note (f = 128 Hz) is sounded on a piano. If the length of the piano wire is 1.00 m and its mass density is 5.00 g/m, what is the tension in the wire?

An earthquake emits both P waves and S waves that travel at different speeds through the Earth. Suppose a P wave travels at 8000 m/s and an S wave at 4000 m/s. If P waves are received at a seismic station 20.0 s before an S wave arrives, how far is the station from the earthquake center?

If a guitar string has a fundamental frequency of 250 Hz, what is the frequency of its third harmonic?

Are the P waves and the S waves associated with earthquakes transverse or longitudinal?

A string of length L with fixed ends is made to go into standing wave patterns. What is the longest wavelength associated with all possible standing wave patterns in this situation?

If the tension on a guitar string is increased by a factor of 2, the fundamental frequency at which it vibrates is changed by what factor?

A standing wave is set up in a 100-cm string fixed at both ends. The string vibrates in 5 distinct segments when driven by a 120-Hz source. What is the wavelength?

A string with fixed ends is made to go into standing wave patterns. At a given tension, the lowest frequency for which such a pattern exists is 150 Hz. Which of the following frequencies would also cause a standing wave pattern in this case?

How many nodes does a standing wave in a string have at the frequency of the sixth harmonic?

If I double the mass per unit length of guitar string, its natural frequency changes by what factor?

For a standing wave on a string, the wavelength must equal:

The lowest A on a piano has a frequency of 27.5 Hz. If the tension in the 2.0-m long string is 151 N and one-half wavelength occupies the string, what is the mass of the string?

A standing wave is set up in a 2.0-m string fixed at both ends. The string vibrates in 3 distinct segments when driven by a 120-Hz source. In how many distinct standing wave segments will the string vibrate if the tension is increased by a factor of 4?