Deck 16: Waves in One Dimension

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

Answer 1

0.25 Hz

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.

Answer 2

V.

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

Answer 3

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

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.

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

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.

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.

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.

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.

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

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

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.

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.

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?

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

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

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

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.

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

Question 21

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.

Question 22

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

Question 23

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.