Question 1

The figure shows the displacement y of a wave at a given position as a function of time and the displacement of the same wave at a given time as a function of position.Determine the frequency of the wave. 
A) 4.0 Hz
B) 0.50 Hz
C) 3.0 Hz
D) 0.33 Hz
E) 0.25 Hz

Accepted Answer

E

Question 2

When a weight W is hanging from a light vertical string,the speed of pulses on the string is V.If a second weight W is added without stretching the string,the speed of pulses on this string will now become
A) 2V.
B)  V.
C) V.
D) V/ 
E) V/2.

Accepted Answer

B

Question 3

In the figure,which of the curves best represents the variation of wave speed as a function of tension for transverse waves on a stretched string? 
A) A
B) B
C) C
D) D
E) E

Accepted Answer

B

Question 4

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 a wave on a string: v = sqrt(T/μ), where v is the wave speed, T is the tension, and μ is the linear mass density. First, calculate μ using the density and cross-sectional area of the wire. Then, solve for T using the given wave speed. The correct tension is approximately 52 N.

Question 5

For the wave shown in the figure,the frequency is 
A) 0.5 Hz.
B) 1 Hz.
C) 2 Hz.
D) 4 Hz.
E) unable to be determined from the given information.

Accepted Answer

Frequency is defined as the number of cycles of a wave that occur in one second. In the given wave, one complete cycle consists of two peaks and one trough. From the graph, we can see that one complete cycle takes 2 seconds. Therefore, the frequency of the wave is:

frequency = number of cycles/ time

frequency = 1/2 = 0.5 Hz

Hence, the best choice is A) 0.5 Hz.

Question 6

The figure shows the displacement y of a traveling wave at a given position as a function of time and the displacement of the same wave at a given time as a function of position. How fast is the wave traveling? 
A) 3.0 m/s
B) 0.75 m/s
C) 0.66 m/s
D) 1.5 m/s
E) 2.0 m/s

Accepted Answer

The answer of The figure shows the displacement y of...

Question 7

A wave pulse traveling to the right along a thin cord reaches a discontinuity where the rope becomes thinner and lighter.What is the orientation of the reflected and transmitted pulses?
A) Both pulses are right side up.
B) The reflected pulse returns right side up while the transmitted pulse is inverted.
C) The reflected pulse returns inverted while the transmitted pulse is right side up.
D) Both pulses are inverted.

Accepted Answer

The answer of A wave pulse traveling to the right...

Question 8

For the wave shown in the figure,the wavelength is 
A) 8 m.
B) 4 m.
C) 2 m.
D) 1 m.
E) unable to be determined from the given information.

Accepted Answer

The answer of For the wave shown in the figure,the...

Question 9

Four traveling waves are described by the following equations,where all quantities are measured in SI units and y represents the displacement.
I: y = 0.12 cos(3x - 21t)
II: y = 0.15 sin(6x + 42t)
III: y = 0.13 cos(6x + 21t)
IV: y = -0.27 sin(3x - 42t)
Which of these waves have the same period?
A) I and III, and also II and IV
B) I and IV, and also II and III
C) I and II, and also III and IV
D) All of them have the same period.
E) They all have different periods.

Accepted Answer

The answer of Four traveling waves are described by the...

Question 10

A wave pulse traveling to the right along a thin cord reaches a discontinuity where the rope becomes thicker and heavier.What is the orientation of the reflected and transmitted pulses?
A) Both pulses are right side up.
B) The reflected pulse returns right side up while the transmitted pulse is inverted.
C) The reflected pulse returns inverted while the transmitted pulse is right side up.
D) Both pulses are inverted.

Accepted Answer

When a wave pulse reaches a discontinuity with a change in the medium, two types of waves can be produced: a reflected wave and a transmitted wave. The orientation of the reflected and transmitted waves is determined by the contrast in the properties of the two media involved in the wave propagation. In this case, the wave is traveling from a thinner and lighter cord to a thicker and heavier one.
 
When a wave pulse propagates in a heavier medium, it reflects back inverted. Therefore, the reflected pulse will be inverted. On the other hand, when a wave pulse crosses a boundary into a medium of different density, it changes its speed and direction of propagation. If the incident angle is not perpendicular to the boundary, the transmitted wave will be transmitted in the new medium at a different angle than the incident angle. Therefore, the transmitted pulse will be right side up. 
 
Therefore, choice C is the best answer as the reflected pulse returns inverted while the transmitted pulse is right side up.

Question 11

Ocean tides are waves that have a period of 12 hours,an amplitude (in some places)of 1.50 m,and a speed of 750 km/hr.What is the distance between adjacent crests of these waves?
A) 9000 km
B) 32,400 km
C) 9000 m
D) 32,400 m
E) 2500 m

Accepted Answer

The distance between adjacent crests of waves, also known as the wavelength, can be calculated using the formula for wave speed: speed = wavelength / period. Given the speed of 750 km/hr and a period of 12 hours, the wavelength (distance between crests) is 750 km/hr * 12 hr = 9000 km.

Question 12

Find the speed of an ocean wave whose vertical displacement y as a function of time t is given by
Y(x,t)= 3.7 cos(2.2x - 5.6t),where all quantities are in SI units.
A) 2.5 m/s
B) 1.9 m/s
C) 3.5 m/s
D) 4.5 m/s

Accepted Answer

The speed of the wave is given by the coefficient of t in the argument of the cosine function, which is 5.6 m/s.

Question 13

A transverse wave is traveling on a string stretched along the horizontal x-axis.The equation for the vertical displacement y of the string is given by y = 0.0020 cos[π(15x - 52t)],where all quantities are in
SI units.The maximum speed of a particle of the string is closest to
A) 0.33 m/s.
B) 0.43 m/s.
C) 0.53 m/s.
D) 0.64 m/s.
E) 0.74 m/s.

Accepted Answer

The answer of A transverse wave is traveling on a...

Question 14

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 15

The vertical displacement y(x,t)of a string stretched along the horizontal x-axis is given by y(x,t)= (6.00 mm)cos[(3.25 m^-1)x - (7.22 rad/s)t]. (a)What is the minimum time for each complete cycle of the wave? (b)What is the distance between adjacent crests of the wave? (c)How fast does this wave travel?

Accepted Answer

The answer of The vertical displacement y(x,t)of a string stretched...

Question 16

Four traveling waves are described by the following equations,where all quantities are measured in SI units and y represents the displacement.
I: y = 0.12 cos(3x + 2t)
II: y = 0.15 sin(6x - 3t)
III: y = 0.23 cos(3x + 6t)
IV: y = -0.29 sin(1.5x - t)
Which of these waves have the same speed?
A) I and III
B) I and IV
C) II and III
D) I and II
E) III and IV

Accepted Answer

The answer of Four traveling waves are described by the...

Question 17

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 18

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 speed of waves on a string is given by the equation v=sqrt(T/μ), where T is the tension and μ is the linear mass density (mass per unit length) of the string. μ = m/l, where m is the mass of the string and l is its length. Therefore, μ = 0.55 g/m. Substituting this value and the given tension T = 75 N into the above equation gives v = sqrt(75 N/0.55 g/m) ≈ 370 m/s.

Question 19

You are generating traveling waves on a stretched string by wiggling one end.If you suddenly begin to wiggle more rapidly without appreciably affecting the tension,you will cause the waves to move down the string
A) faster than before.
B) slower than before.
C) at the same speed as before.

Accepted Answer

The speed of a wave on a string depends on the tension in the string and the mass per unit length of the string, not on the frequency with which the wave is generated. Therefore, wiggling more rapidly without changing the tension does not affect the speed of the waves.

Question 20

The figure shows the displacement y of a traveling wave at a given position as a function of time and the displacement of the same wave at a given time as a function of position.Determine the wavelength of the wave. 
A) 2.0 cm
B) 3.0 m
C) 2.0 m
D) 4.0 m
E) 1.5 m

Accepted Answer

The answer of The figure shows the displacement y of...

Quiz 16: Waves in One Dimension

The figure shows the displacement y of a wave at a given position as a function of time and the displacement of the same wave at a given time as a function of position.Determine the frequency of the wave.

When a weight W is hanging from a light vertical string,the speed of pulses on the string is V.If a second weight W is added without stretching the string,the speed of pulses on this string will now become

In the figure,which of the curves best represents the variation of wave speed as a function of tension for transverse waves on a stretched string?

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?

For the wave shown in the figure,the frequency is

The figure shows the displacement y of a traveling wave at a given position as a function of time and the displacement of the same wave at a given time as a function of position. How fast is the wave traveling?

A wave pulse traveling to the right along a thin cord reaches a discontinuity where the rope becomes thinner and lighter.What is the orientation of the reflected and transmitted pulses?

For the wave shown in the figure,the wavelength is

Four traveling waves are described by the following equations,where all quantities are measured in SI units and y represents the displacement. I: y = 0.12 cos(3x - 21t) II: y = 0.15 sin(6x + 42t) III: y = 0.13 cos(6x + 21t) IV: y = -0.27 sin(3x - 42t) Which of these waves have the same period?

A wave pulse traveling to the right along a thin cord reaches a discontinuity where the rope becomes thicker and heavier.What is the orientation of the reflected and transmitted pulses?

Ocean tides are waves that have a period of 12 hours,an amplitude (in some places) of 1.50 m,and a speed of 750 km/hr.What is the distance between adjacent crests of these waves?

Find the speed of an ocean wave whose vertical displacement y as a function of time t is given by Y(x,t) = 3.7 cos(2.2x - 5.6t) ,where all quantities are in SI units.

A transverse wave is traveling on a string stretched along the horizontal x-axis.The equation for the vertical displacement y of the string is given by y = 0.0020 cos[π(15x - 52t) ],where all quantities are in SI units.The maximum speed of a particle of the string is closest to

Four traveling waves are described by the following equations,where all quantities are measured in SI units and y represents the displacement. I: y = 0.12 cos(3x + 2t) II: y = 0.15 sin(6x - 3t) III: y = 0.23 cos(3x + 6t) IV: y = -0.29 sin(1.5x - t) Which of these waves have the same speed?

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?

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?

You are generating traveling waves on a stretched string by wiggling one end.If you suddenly begin to wiggle more rapidly without appreciably affecting the tension,you will cause the waves to move down the string

The figure shows the displacement y of a traveling wave at a given position as a function of time and the displacement of the same wave at a given time as a function of position.Determine the wavelength of the wave.