Deck 15: Waves

Question 1

A string is 80.0 cm long and has a mass per unit length of 5.51 * 10^-4 kg/m.The tension in the string is 200 N.In the fundamental mode,at what frequency does the string vibrate?

A)376 Hz
B)450 Hz
C)598 Hz
D)702 Hz
E)964 Hz

Answer 1

376 Hz

Question 2

A horizontal transverse standing wave has a wavelength of 12.0 cm.What is the horizontal distance between adjacent nodes and anti-nodes?

A)1.00 cm
B)2.00 cm
C)3.00 cm
D)6.00 cm

Answer 2

3.00 cm

Question 3

The amplitude,angular frequency,and wave number of a transverse traveling wave are 4.00 m,12.0 rad/s,and 4.00 rad/m,respectively.At what speed does it transfer energy from place to place?

A)0.333 m/s
B)3.00 m/s
C)16.0 m/s
D)48.0 m/s

Answer 3

3.00 m/s

Question 4

An 80 cm long string,fixed at both ends vibrates at a fundamental frequency of 450 Hz and has a mass per unit length of 5.51 * 10^-4 kg/m.What is the tension in the string?

A)200 N
B)191 N
C)320 N
D)231 N
E)286 N

Question 5

Two adjacent frequencies of transverse standing waves on a string held fixed at both ends are 1440 Hz and 1560 Hz.What is the fundamental frequency of the transverse standing waves on this string?

A)60 Hz
B)120 Hz
C)180 Hz
D)240 Hz

Question 6

A 10.0-m long string of mass 20.0 g is clamped at both ends.The tension in the string is 200 N.The string is pluck so that it oscillates.What is the wavelength of the wave if it produces a standing wave with 2 antinodes?

A)2.00 m
B)3.75 m
C)7.0 m
D)10.0 m
E)15.0 m

Question 7

Which of the following functions is not a solution to the Wave Equation?

A)y(x,t)=
B)y(x,t)=
C)y(x,t)=
D)y(x,t)=

Question 8

You increase the tension in a string to four times its current value.This results in increasing the speed of the wave in the string by a factor of

A)1.
B) .
C)2.
D)3.
E)

Question 9

A 5.00-m long string of mass 10.0 g is clamped at both ends.The tension in the string is 200 N.The string is pluck so that it oscillates and the speed of a wave on the string is 150 m/s.What is the frequency of the wave if it produces a standing wave with 4 antinodes?

A)31 Hz
B)45 Hz
C)60 Hz
D)79 Hz
E)84 Hz

Question 10

What is the radius of a brass wire having a wave speed of 225 m/s when stretched with a tension of 150 N? The density of brass is 8.60 * 10³ kg/m³.

A)0.750 mm
B)0.563 mm
C)0.412 mm
D)0.331 mm
E)0.287 mm

Question 11

You increase the tension in a string to double its current value.This results in increasing the speed of the wave in the string by a factor of

A)1.
B) .
C)2.
D)3.
E)

Question 12

The Sun emits light waves in all directions.When this light reaches the Earth,its intensity is 1350 W/m².What is its intensity when it reaches Mars? The distance from the Sun to the Earth is 1.50 * 10¹¹ m and the distance from the Sun to Mars is 2.28 * 10¹¹m.

A)584 W/m²
B)888 W/m²
C)2050 W/m²
D)3120 W/m²

Question 13

One of the main mechanisms that humans use to determine whether a sound is coming from the left or the right is based on the fact that the sound may reach one ear before the other.Given that the speed of sound in air is 343 m/s and that human ears are typically 20 cm apart,what is the time resolution in human hearing that would allow sounds coming from the left to be distinguished from sounds coming from the right using this mechanism?

A)2.92 * 10^-4 s
B)5.83 * 10^-4 s
C)1.17 * 10^-3 s
D)7.45 * 10^-3 s
E)9.67 * 10^-3 s

Question 14

A string,fixed at both ends vibrates at a fundamental frequency of 450 Hz and has a mass per unit length of 5.51 * 10^-4 kg/m.The tension in the string is 200 N.What is the length of the string?

A)53 cm
B)80 cm
C)67 cm
D)92 cm
E)120 cm

Question 15

The wave speed in a brass wire with a radius of 0.750 mm is 340 m/s.What is the tension in the wire? The density of brass is 8.60 * 10³ kg/m³.

A)2320 N
B)250 N
C)1900 N
D)2900 N
E)1760 N

Question 16

The wave speed in a wire stretched with a tension of 250 N is 240 m/s and the radius of the wire is 0.50mm.What is the density of the wire?

A)3.94 * 10³ kg/m³
B)4.01 * 10³ kg/m³
C)2.75 * 10³ kg/m³
D)5.53 * 10³ kg/m³
E)8.60 * 10³ kg/m³

Question 17

A 5.00-m long string is clamped at both ends.The tension in the string is 200 N.The string is pluck so that it oscillates and the speed of a wave on the string is 150 m/s.What is the mass of the string?

A)3.5 g
B)15.7 g
C)23.3 g
D)36.7 g
E)44.4 g

Question 18

What is the wave speed in a brass wire with a radius of 0.750 mm stretched with a tension of 250 N? The density of brass is 8.60 * 10³ kg/m³.

A)136 m/s
B)340 m/s
C)128 m/s
D)257 m/s
E)56.9 m/s

Question 19

A wave on a string has a wave function given as .What is the speed of the wave?

A)2.38 * 10^-1 m/s
B)4.12 * 10^-1 m/s
C)7.58 * 10^-1 m/s
D)8.08 * 10^-1 m/s

Question 20

Bob is talking to Alice using a tin can telephone,which consists of two steel cans connected by a 15.5-m long stretched steel wire.The wire has a linear density of 6.13 g/m and the tension in the wire is 32.4 N.The sound waves leave Bob's mouth,are collected by the can on the left,and then create vibrations in the wire,which travel to Alice's can,and are then transformed back into sound waves in air.How long does it take for the wave traveling in the wire to reach Alice?

A)0.0452 s
B)14.3 s
C)0.156 s
D)0.678 s
E)0.213 s

Question 21

A wave of amplitude 30 cm travels with a velocity of 10 m/s and a frequency of 10 Hz.What is its wavelength?

A)3 m
B)2 m
C)10 m
D)30 m
E)1 m

Question 22

A wave of amplitude 30 cm,wavelength of 0.75 m and frequency 20 Hz.What is its speed?

A)6.0 m/s
B)10 m/s
C)27 m/s
D)15 m/s
E)67 m/s

Question 23

An earthquake creates a wave in a canal.If the canal is 3.2 km long and 210 m deep,what is the speed of the waves created by the earthquake in the water?

A)29 m/s
B)2100 m/s
C)14 m/s
D)45 m/s
E)180 m/s

Question 24

A transverse harmonic wave of wavelength 14.5 cm and a frequency of 488 Hz travels along the positive z direction on a string.The wave oscillations take place in the x-z plane with an amplitude of 3.00 cm.The speed of the wave is

A)24.8 m/s.
B)36.2 m/s.
C)70.8 m/s.
D)84.6 m/s.
E)98.7 m/s.

Question 25

The first harmonic of a standing wave is set up in a 3-m string with a mass of 100 g and a tension of 100 N.What is the frequency of the harmonic?

A)10.4 Hz
B)9.1 Hz
C)3.5 Hz
D)15.2 Hz
E)8.3 Hz

Question 26

A rock is thrown into a pond and produces a series of waves.One meter away from the impact point the first wave is 3.0 cm high.How high will that wave be 2.0 m away from the impact point?

A)0.75 cm
B)1.1 cm
C)1.5 cm
D)2.1 cm

Question 27

A 2.45-m long wire of uniform linear mass density hangs from the ceiling.How long will it takes for a pulse to travel the length of the wire?

A)2.0 s
B)2.2 s
C)0.5 s
D)0.2 s
E)1.0 s

Question 28

A traveling sinusoidal wave moves to the right at a speed of v₁ and with a wavelength of along String 1,which has a linear mass density $\mu$ ₁.String 1 is attached to a heavier String 2 (with linear mass density $\mu$ ₂ = 4 $\mu$ ₁)and the wave in String 1 produces a traveling wave in String 2,which also moves to the right.What is the wavelength of the wave in String 2 in terms of ?

A)
B)4
C)0.25
D)0.50
E)2

Question 29

A sinusoidal wave travels along a stretched string.A point along the string has a maximum velocity of 1 m/s and a maximum displacement of 2 cm.What is the maximum acceleration at that point?

A)10 m/s²
B)50 m/s²
C)30 m/s²
D)15 m/s²
E)20 m/s²

Question 30

A rock is thrown into a pond and produces a series of waves.One meter away from the impact point the first wave is 3.0 cm high.How far from the impact point will that wave have a height of 1.5 cm?

A)3.0 m
B)2.0 m
C)1.4 m
D)4.0 m

Question 31

If the speed of gravity waves is the same a for light (3.00 * 10⁸ m/s),as is thought to be the case,find the fundamental frequency of waves that would be detected by LIGO (distance between the two end points is 3002 km).

A)50 Hz
B)100 Hz
C)200 Hz
D)900 Hz
E)Gravity waves,unlike electromagnetic waves,do not have a frequency.

Question 32

In the figure,point A is 30 cm below the ceiling.Determine how much longer it will take for a pulse to travel along wire 1 than it would along wire 2.Both wires are made of the same material and have identical cross sections.

A)3.48 times longer
B)1.56 times longer
C)2.28 times longer
D)1.71 times longer
E)0.58 times longer

Question 33

A wire of uniform linear mass density hangs from the ceiling.It takes 1 s for a pulse to travel the length of the wire.How long is the wire?

A)1.23 m
B)0.78 m
C)0.56 m
D)2.45 m
E)3.65 m

Question 34

A wave is described by the equation y = 3sin(4t - 3x + 2).What is the velocity of the wave?

A)0.5 m/s
B)2.0 m/s
C)1.0 m/s
D)1.3 m/s
E)0.7 m/s

Question 35

The tension in a 3.4 m long,1.0-cm diameter steel cable ( )under 480 N.What is the fundamental frequency of vibration of the cable?

A)0.036 Hz
B)0.072 Hz
C)2.1 Hz
D)4.1 Hz
E)8.2 Hz

Question 36

A wave of amplitude 30 cm travels with a velocity of 10 m/s and a wavelength of 0.25 m.What is its frequency?

A)33 Hz
B)2.5 Hz
C)25 Hz
D)40 Hz
E)50 Hz

Question 37

A wave travels in positive x direction at 30.0 m/s along a string in the positive x direction.The frequency of the wave is 50.0 Hz.Which of the following could the equation to describe this wave?

A)
B)
C)
D)
E)None are correct.

Question 38

A standing wave is set up on a 3-m long string with a vibrational frequency of 100 Hz.Which of the following is a possible velocity for the wave?

A)125 m/s
B)175 m/s
C)200 m/s
D)225 m/s
E)All are correct.

Question 39

A traveling wave is represented by the function f(x,y)= (5.3 cm)e^{((6.8 rad/s)t + (4.3 rad/m)x -2.1 rad)} + (3.5cm)y.What is the velocity of the traveling wave?

A)0.36 m/s in the x direction
B)0.36 m/s in the y direction
C)0.36 m/s in the negative x direction
D)1.6 m/s in the negative x direction
E)1.6 m/s in the x direction

Question 40

A 2-m string with a mass of 100 g has an applied tension of 100 N while it is plucked.How long does it take the resulting wave to go from one end of the string to the other?

A)29 ms
B)121 ms
C)68 ms
D)45 ms
E)81 ms

Question 41

You are standing in the very center of a deep,flat-bottomed valley,and shout "Hello!" If the speed of sound is 343 m/s,and you hear the second echo "Hello!" at 2.1 seconds after you shout,how wide is the valley?

A)360 m
B)180 m
C)720 m
D)540 m

Question 42

A violinist is trying to tune her instrument to 512 Hz,but it is at 491.By what percent does she have to change the tension to tune the violin?

A)1.2%
B)4.1%
C)8.7%
D)12.1%
E)14.5%

Question 43

Two wires made of the same material have same length and the tension.Their diameters are 1 mm (wire 1)and 0.5 mm (wire 2).The ratio f₂/f₁ of their fundamental frequencies is

A)0.10.
B)0.25.
C)0.5.
D)1.0.
E)2.0

Question 44

A sonar generator on a ship produces a sound wave with a frequency of 2.45 MHz and a wavelength of 5.9 * 10^-4 m.The generator is pointed straight down and emits a pulse.The echo of this pulse is received 5.08 s later.How deep is the ocean at this point?

A)34.5 m
B)121 m
C)3670 m
D)8810 m
E)51,200 m

Question 45

Seismic waves created by earthquakes travel both as longitudinal or compression waves and as transverse waves.These waves travel

A)along the surface of the Earth.
B)inside the volume of the Earth.
C)both along the surface and inside the volume of the Earth.
D)in the air.

Question 46

The vertical displacement due to a traveling wave moving horizontally is given by y(x,t)= 5.4 cos (0.4(rad/cm)x - 45(rad/s)t (sec))where x and y are in centimeters.The horizontal distance between the points whose phase differs by $\pi$ /3 rad is

A)1.05 cm.
B)2.62 cm.
C)7.86 cm.
D)9.81 cm.
E)13.6 cm.

Question 47

I sit in a boat on a lake and watch water waves pass.I count 1.5 s for the wave crests to travel the length of my (stationary)4.5-m long boat.The time between successive crests is 0.5 s.What is the wavelength of the waves?

A)0.5 m
B)1.0 m
C)1.5 m
D)2.0 m
E)2.5 m

Question 48

A guitar string with a mass of 12 g is 80 cm long and attached to a guitar at two points separated by 71 cm.What tension must the guitar string have so that its fundamental note is 256 Hz?

A)500 N
B)550 N
C)1100 N
D)2000 N
E)2200 N

Question 49

A string of mass 3 g and length 1 m can carry a wave of 20 mW power.The amplitude of the wave is 3.25 mm.What is the period of oscillation if the tension applied to the string is 42 N?

A)78 ms
B)40 ms
C)68 ms
D)73 ms
E)61 ms

Question 50

A string is stretched between two fixed points.A standing wave is set up on the string.The string is vibrating in its fifth harmonic mode.Which one of the following statements is true?

A)There are five nodes visible (including the ends).
B)There are five antinodes visible.
C)There are seven nodes visible (including the ends).
D)There are six antinodes visible.
E)There are four antinodes visible.

Question 51

An electromagnetic wave moves with the velocity of light,c = 3.0 * 10⁸ m/s.If it has a wavelength of 1.5 * 10^-6 m,what is its frequency?

A)4.5 * 10² s
B)0.5 * 10^-14 s
C)2 * 10¹⁴ s^-1
D)4.5 * 10^-2 s^-1
E)1.5 * 10^-2 s

Question 52

If transverse waves on a string travel with a velocity of 20 m/s when the string is under a tension of 30 N,what tension will be required for the waves to travel with a velocity of 40 m/s on the same string?

A)7.5 N
B)15 N
C)42 N
D)60 N
E)120 N

Question 53

A string of mass 3 g and length 1 m can carry a wave of 20 mW power.When a tension of 15 N is applied to the string it oscillates with a period of 40 ms.The amplitude of the wave is

A)2.76 mm.
B)9.80 mm.
C)11.8 mm.
D)18.5 mm.
E)23.5 mm.

Question 54

The equation representing a wave on a string is y(x,t)= 0.23 m cos((23.2 m^-1)x - (15.3s^-1)t).What is the wave velocity?

A)1.5 m/s right
B)0.66 m/s right
C)1.5 m/s left
D)0.66 m/s left
E)None are correct.

Question 55

A stretched string with a mass of 50 g and a length of 120 cm is placed under a tension of 230 N.How much power must be supplied to the string to generate traveling waves that have a frequency of 90 Hz and an amplitude of 7.0 cm?

A)61 W
B)170 W
C)280 W
D)2400 W
E)2600 W

Question 56

A string is stretched between two fixed points and has a fundamental frequency of 100 Hz.If the tension is unchanged,then the frequency of the mode shown is

A)100.
B)200.
C)300.
D)400.
E)800.

Question 57

A string of mass 3 g and length 1 m can carry a wave of 20 mW power.The amplitude of the wave is 2.25 mm.What is the tension applied to the string if it oscillates with a period of 40 ms.

A)38 N
B)34 N
C)41 N
D)20 N
E)44 N

Question 58

A guitar string with a mass of 12 g is 80 cm long and attached to the guitar at two points separated by 65 cm.What is the frequency of its fundamental note when it is placed under a tension of 170 N?

A)74 Hz
B)82 Hz
C)93 Hz
D)150 Hz
E)160 Hz

Question 59

A guitar string has a tension on it of 6500 N and length of 1.2 m.If the fundamental frequency of the string is 440 Hz,what is the linear mass density of the string?

A)5.8 g/m
B)7.0 g/m
C)8.4 g/m
D)23 g/m
E)Something else.

Question 60

You are standing in the very center of a deep,flat-bottomed valley,and shout "Hello!" If the valley is 355 m wide,and the speed of sound is 343 m/s,when do you hear the first echo "Hello!"?

A)1.03 s
B)0.517 s
C)1.93 s
D)0.966 s

Question 61

How long does it take for light to travel from the Sun to Earth? (Hint: The distance between Earth and Sun is 148 Million km,the speed of light is 300,000 km/s.)

A)less than 8 s
B)about 8 s
C)about 8 minutes
D)about 8 hours
E)more than 8 hours