Deck 13: Vibrations and Waves

Question 1

Two springs,each with spring constant k,are attached end to end in a series fashion.A second pair of identical springs are also attached in series fashion.Then the pair of series attached springs are attached in parallel to each other.What is the effective spring constant of the resulting combination of springs?

A) k/2
B) 2k
C) either k/4 or 4k
D) k

Answer 1

k

Question 2

A mass of 4.4 kg,resting on a horizontal frictionless surface,is attached on the right to a horizontal spring with spring constant 26 N/m and on the left to a horizontal spring with spring constant 58 N/m.If this system is moved from equilibrium,what is the effective spring constant?
​

A) -32 N/m
B) 32 N/m
C) 84 N/m
D) -84 N/m
E) ​16 N/m

Answer 2

84 N/m

Question 3

Two springs,each with spring constant 10 N/m,are connected in parallel,and the combination is hung vertically from one end.A 20-N weight is then suspended from the other end of the combined spring.How far does the combined spring stretch as it comes to equilibrium?
​

A) 2 m
B) 0.5 m
C) 4 m
D) 1 m
E) 8 m

Answer 3

1 m

Question 4

Which is not an example of approximate simple harmonic motion?

A) A ball bouncing on the floor.
B) A child swinging on a swing.
C) A piano string that has been struck.
D) A car's radio antenna as it waves back and forth.

Question 5

A 0.36-kg object is oscillating on a spring with a spring constant of k = 18 N/m.What is the potential energy of the system when the object displacement is 0.041 m,exactly half the maximum amplitude?
​

A) zero
B) 0.03 0 J
C) 0.015 J
D) 0.369 J
E) ​9 J

Question 6

Three identical springs each have the same spring constant k.If these three springs are attached end to end forming a spring three times the length of one of the original springs,what will be the spring constant of the combination?

A) k
B) 3 k
C) k/3
D) 1.73 k

Question 7

A mass of 0.4 kg,hanging from a spring with a spring constant of 87 N/m,is set into an up-and-down simple harmonic motion.What is the speed of the mass when moving through a point at 0.05 m displacement? The starting displacement of the mass is 0.1 m from its equilibrium position.

A) zero
B) 0.6 m/s
C) 0.7 m/s
D) 1.3 m/s
E) ​1.8 m/s

Question 8

A 0.25-kg object is attached to a spring with spring constant k = 10 N/m and moves with simple harmonic motion over a horizontal frictionless surface.At the instant that it is displaced from equilibrium by −0.051 m,what is its acceleration?
​

A) 1,275 m/s²
B) −127.5 m/s²
C) 0.1 m/s²
D) 2 m/s²
E) ​0.5 m/s²

Question 9

The SI base units for spring constant are which of the following?

A) kg⋅s²
B) kg/m²
C) kg/s²
D) kg⋅m²

Question 10

Doubling the displacement from equilibrium of an object in simple harmonic motion will bring about a change in the magnitude of the object's acceleration by what factor?
​

A) 0.5
B) 1.0
C) 2.0
D) 4
E) ​0.25

Question 11

Suppose there is an object for which F = +kx.What will happen if the object is moved away from equilibrium (x = 0)and released?

A) It will return to the equilibrium position.
B) It will move further away with constant velocity.
C) It will move further away with constant acceleration.
D) It will move further away with increasing acceleration.

Question 12

A mass of 0.4 kg,attached to a spring with a spring constant of 80 N/m,is set into simple harmonic motion.What is the magnitude of the acceleration of the mass when at its maximum displacement of 0.2 m from the equilibrium position?
​

A) zero
B) 20 m/s²
C) 10 m/s²
D) 40 m/s²
E) ​80 m/s²

Question 13

Tripling the weight suspended vertically from a coil spring will result in a change in the displacement of the spring's lower end by what factor?
​

A) 0.33
B) 1.0
C) 3.0
D) 9.0
E) ​0.11

Question 14

Spring #1 has spring constant 80 N/m.Spring #2 has an unknown spring constant,but when connected in series with Spring #1,the connected springs have an effective force constant of 10 N/m.What is the spring constant for Spring #2?
​

A) 70 N/m
B) 90 N/m
C) 9 N/m
D) 11 N/m
E) ​85 N/m

Question 15

A mass of 0.39 kg,hanging from a spring with a spring constant of 72 N/m,is set into an up-and-down simple harmonic motion.What is the speed of the mass when moving through the equilibrium point? The starting displacement from equilibrium is 0.14 m.
​

A) zero
B) 1.9 m/s
C) 2.7 m/s
D) 2.5 m/s
E) 0.3 m/s

Question 16

If it takes 3 N to stretch a spring 6 cm and if the spring is then cut in half,what force does it take to stretch one of the halves 3 cm?
​

A) 1.5 N
B) 3 N
C) 6 N
D) 9 N
E) ​12 N

Question 17

A 0.39 kg object,attached to a spring with spring constant k = 15 N/m,is moving on a horizontal frictionless surface in simple harmonic motion of amplitude of 0.082 m.What is its speed at the instant when its displacement is 0.041 m? (Hint: Use conservation of energy. )
​

A) 4.4 m/s
B) 8.8 m/s
C) 44 cm/s
D) 56.9 cm/s
E) ​31.1 cm/s

Question 18

A large spring requires a force of 190 N to compress it only 0.010 m.What is the spring constant of the spring?
​

A) 19 N/m
B) 19,000 N/m
C) 1.9 N/m
D) 188 N/m
E) ​9,500 N/m

Question 19

A runaway railroad car,with mass 36 × 10⁴ kg,coasts across a level track at 2.7 m/s when it collides with a spring-loaded bumper at the end of the track.If the spring constant of the bumper is 2.7 × 10⁶ N/m,what is the maximum compression of the spring during the collision? (Assume the collision is elastic. )

A) 0.99 m
B) 1.39 m
C) 0.7 m
D) 1.88 m
E) 1.97 m

Question 20

A tiny spring,with a spring constant of 1.3 N/m,will be stretched to what displacement by a 0.005-N force?
​

A) 3.8 mm
B) 7.7 mm
C) 11.5 mm
D) 6.5 mm
E) ​3.3 mm

Question 21

Suppose a 0.7-kg mass on a spring that has been compressed 0.1 m has elastic potential energy of 1.5 J.How much further must the spring be compressed to triple the elastic potential energy?
​

A) 0.17 m
B) 0.27 m
C) 0.3 m
D) 0.07 m
E) 0.2 m

Question 22

By what factor must one change the weight suspended vertically from a spring coil in order to five times its period of simple harmonic motion?
​

A) 1/25
B) 0.2
C) 5.0
D) 25.0
E) ​1.0

Question 23

The motion of a piston in an automobile engine is nearly simple harmonic.If the 1-kg piston travels back and forth over a total distance of 11.9 cm,what is its maximum speed when the engine is running at 3,540 rpm?
​

A) 22.06 m/s
B) 11.03 m/s
C) 44.11 m/s
D) 5.51 m/s
E) ​2.76 m/s

Question 24

For a mass suspended on a spring in the vertical direction,the time for one complete oscillation will depend on:

A) the value for g (the acceleration due to gravity).
B) the distance the mass was originally pulled down.
C) the maximum speed of the oscillating mass.
D) the time doesn't depend on any of the above.

Question 25

Which one of the following quantities is at a maximum when an object in simple harmonic motion is at its maximum displacement?

A) speed
B) acceleration
C) kinetic energy
D) frequency

Question 26

Suppose a 0.9-kg mass on a spring that has been compressed 0.1 m has elastic potential energy of 1.1 J.What is the spring constant?
​

A) 198 N/m
B) 244 N/m
C) 220 N/m
D) 22 N/m
E) ​90 N/m

Question 27

A 0.34-kg block rests on a frictionless level surface and is attached to a horizontally aligned spring with a spring constant of 55 N/m.The block is initially displaced 4.1 cm from the equilibrium point and then released to set up a simple harmonic motion.What is the speed of the block when it passes through the equilibrium point?
​

A) 2.58 m/s
B) 0.74 m/s
C) 1.82 m/s
D) 0.52 m/s
E) ​2.35 m/s

Question 28

A mass on a spring vibrates in simple harmonic motion at a frequency of 3.9 Hz and an amplitude of 7.8 cm.If a timer is started when its displacement is a maximum (hence x = 7.8 cm when t = 0),what is the displacement of the mass when t = 3.4 s?
​

A) zero
B) -0.005 m
C) 0.079 m
D) -1.239 m
E) ​-0.01 m

Question 29

A mass on a spring vibrates in simple harmonic motion at a frequency of 2 Hz and an amplitude of 7 cm.If a timer is started when its displacement is a maximum (hence x = 7 cm when t = 0),what is the speed of the mass when t = 7 s?
​

A) zero
B) 87.965 m/s
C) 9.016 m/s
D) 7 m/s
E) ​43.982 m/s

Question 30

A 0.36-kg block rests on a frictionless level surface and is attached to a horizontally aligned spring with a spring constant of 40 N/m.The block is initially displaced 6 cm from the equilibrium point and then released to set up a simple harmonic motion.A frictional force of 0.3 N exists between the block and surface.What is the speed of the block when it passes through the equilibrium point after being released from the 6-cm displacement point?
​

A) 0.55 m/s
B) 0.39 m/s
C) 0.77 m/s
D) 0.3 m/s
E) 2.19 m/s

Question 31

Suppose a 0.36-kg mass on a spring-loaded gun that has been compressed 0.2 m has elastic potential energy of 1.9 J.How high above the spring's equilibrium point can the gun fire the mass if the gun is fired straight up?
​

A) 0.54 m
B) 0.88 m
C) 0.34 m
D) 5.08 m
E) 51.52 m

Question 32

The oxygen molecule (O₂)may be regarded as two masses connected by a spring.In vibrational motion,each oxygen atom alternately approaches,then moves away from the center of mass of the system.If each oxygen atom of mass m = 2.67 × 10−²⁶ kg has a vibrational energy of 1.6 × 10−²¹ J and the effective spring constant is 100 N/m,then what is the amplitude of oscillation of each oxygen atom?
​

A) 3.2 × 10−¹¹ m
B) 1.6 × 10−¹¹ m
C) 1.1 × 10−¹¹ m
D) 5.7 × 10−¹² m
E) ​4 × 10−¹² m

Question 33

A car with bad shocks bounces up and down with a period of 1.62 s after hitting a bump.The car has a mass of 1,600 kg and is supported by four springs of force constant k.What is k for each spring?
​

A) 6,017 N/m
B) 1,504 N/m
C) 1,551 N/m
D) 3,009 N/m
E) ​788 N/m

Question 34

A 0.25-kg mass is oscillating on a spring over a horizontal frictionless surface.When it is at a displacement of 2.8 cm for equilibrium it has a kinetic energy of 1.4 J and a spring potential energy of 2.3 J.What is the maximum speed of the mass during its oscillation?
​

A) 3.8 m/s
B) 0.2 m/s
C) 5.4 m/s
D) 4.7 m/s
E) ​3.4 m/s

Question 35

An object is attached to a spring and its frequency of oscillation is measured.Then another object is connected to the first object,and the resulting mass is three times the original value.By what factor is the frequency of oscillation changed?
​

A) 1/3
B) 0.58
C) 1/9
D) 3
E) ​9

Question 36

An ore car of mass 4,700 kg rolls downhill on tracks from a mine.At the end of the tracks,11.1 m lower in elevation,is a spring with k = 410,000 N/m.How much is the spring compressed in stopping the ore car? Ignore friction.
​

A) 1.12 m
B) 0.79 m
C) 1.58 m
D) 0.5 m
E) ​0.47 m

Question 37

A mass on a spring vibrates in simple harmonic motion at a frequency of 4.2 Hz and an amplitude of 4.2 cm.If a timer is started when its displacement is a maximum (hence x = 4.2 cm when t = 0),what is the acceleration magnitude when t = 4 s?
​

A) zero
B) 0.3 m/s²
C) 18.1 m/s²
D) 9 m/s²
E) ​11.8 m/s²

Question 38

A mass on a spring vibrates in simple harmonic motion at a frequency of 4.4 Hz and an amplitude of 8.6 cm.If the mass of the object is 0.4 kg,what is the spring constant?
​

A) 11 N/m
B) 764 N/m
C) 306 N/m
D) 36 N/m
E) ​657 N/m

Question 39

An object moving in simple harmonic motion has an amplitude of 0.05 m and a maximum acceleration of 40 m/s².What is the frequency of the system?
​

A) 14.1 Hz
B) 177.7 Hz
C) 4.5 Hz
D) 11.3 Hz
E) ​2 Hz

Question 40

I attach a 2.9-kg block to a spring that obeys Hooke's Law and supply 19 J of energy to stretch the spring.I release the block;it oscillates with period 0.35 s.The amplitude is:
​

A) 14 cm.
B) 20 cm.
C) 10 cm.
D) 85 cm.
E) ​29 cm.

Question 41

By what factor should the length of a simple pendulum be changed if the period of vibration were to be two times?
​

A) 1/4
B) 0.5
C) 2
D) 4
E) ​1.0

Question 42

For a wave on the ocean,the amplitude is:

A) the distance between crests.
B) the height difference between a crest and a trough.
C) one half the height difference between a crest and a trough.
D) how far the wave goes up on the beach.

Question 43

The wavelength of a traveling wave can be calculated if one knows the:

A) frequency.
B) speed and amplitude.
C) amplitude and frequency.
D) frequency and speed.

Question 44

When car shock absorbers wear out and lose their damping ability,what is the resulting oscillating behavior?

A) underdamped
B) critically damped
C) overdamped
D) hyperdamped

Question 45

The position of a 0.72-kg mass undergoing simple harmonic motion is given by x = (0.160 m)cos (πt/16).What is the maximum net force on the mass as it oscillates?
​

A) 4.4 × 10−³ N
B) 27.8 × 10−³ N
C) 6.2 × 10−³ N
D) 22.6 N
E) ​2.3 × 10−³ N

Question 46

If the frequency of a traveling wave train is increased by a factor of three in a medium where the speed is constant,which of the following is the result?

A) amplitude is one third as big
B) amplitude is tripled
C) wavelength is one third as big
D) wavelength is tripled

Question 47

A simple pendulum has a mass of 0.21 kg and a length of 1.9 m.It is displaced through an angle of 36° and then released.After a time,the maximum angle of swing is only 12°.How much energy has been lost to friction?
​

A) 0.66 J
B) 0.75 J
C) 0.09 J
D) 1.00 J
E) 0.83 J

Question 48

A musical tone,sounded on a piano,has a frequency of 480 Hz and a wavelength in air of 0.800 m.What is the wave speed?
​

A) 96 m/s
B) 416 m/s
C) 384 m/s
D) 104 m/s
E) ​307.2 m/s

Question 49

If one could transport a simple pendulum of constant length from the Earth's surface to the Moon's,where the acceleration due to gravity is one-sixth (1/6)that on the Earth,by what factor would the pendulum frequency be changed?

A) about 6.0
B) about 2.5
C) about 0.41
D) about 0.17

Question 50

A simple pendulum has a period of 2.3 s.What is the pendulum length? (g = 9.8 m/s²)
​

A) 5.25 m
B) 4.13 m
C) 1.31 m
D) 0.76 m
E) ​0.19 m

Question 51

The position of a 0.71-kg mass undergoing simple harmonic motion is given by x = (0.160 m)cos (πt/16).What is its position at t = 6.8 s?
​

A) -0.037 m
B) 0.063 m
C) 6.339 m
D) 0.037 m
E) ​0.619 m

Question 52

If a radio wave has speed 3.17 × 10⁸ m/s and frequency 94.8 MHz,what is its wavelength?
​

A) 1.67 m
B) 2.31 m
C) 4.4 m
D) 3.34 m
E) ​6.62 m

Question 53

Consider the curve f(x)= A cos(2πx/λ).The wavelength of the wave will be:

A) the distance 0 to A.
B) twice the distance 0 to A.
C) the distance x₂ to x₃.
D) twice the distance x₂ to x₃.

Question 54

The position of a 0.67-kg mass undergoing simple harmonic motion is given by x = (0.160 m)cos (πt/15).What is its period of oscillation?
​

A) 100 s
B) 30 s
C) 15 s
D) 7.5 s
E) 3.75 s

Question 55

As a gust of wind blows across a field of grain,a wave can be seen to move across the field as the tops of the plants sway back and forth.This wave is a:

A) transverse wave.
B) longitudinal wave.
C) polarized wave.
D) interference of waves.

Question 56

A simple pendulum of length 1.68 m has a mass of 100 g attached.It is drawn back 35.5° and then released.What is the maximum speed of the mass?

A) 1.35 m/s
B) 3.99 m/s
C) 2.87 m/s
D) 1.91 m/s
E) ​0.18 m/s

Question 57

Which of the following is an example of a longitudinal wave?

A) sound wave in air
B) wave traveling in a string
C) both a and b
D) neither a nor b

Question 58

The kinetic energy of the bob on a simple pendulum swinging in simple harmonic motion has its maximum value when the displacement from equilibrium is at what point in its swing?

A) zero displacement
B) 1/4 the amplitude
C) 1/2 the amplitude
D) equal the amplitude

Question 59

Quadruple the mass of the bob on a simple pendulum will cause a change in the frequency of the pendulum swing by what factor?
​

A) 0.25
B) 1.0
C) 16
D) 4
E) ​0.06

Question 60

A traveling wave train has wavelength 0.4 m,speed 34 m/s.Find the wave frequency.
​

A) 0.012 Hz
B) 42.5 Hz
C) 85 Hz
D) 21.25 Hz
E) ​53.759 Hz

Question 61

Double both the tension in a guitar string and its mass per unit length will result in changing the wave speed in the string by what factor?
​

A) 0.71
B) 1.00 (i.e. ,no change)
C) 1.41
D) 2.00
E) ​2.83

Question 62

Quinary the mass per unit length of a guitar string will result in changing the wave speed in the string by what factor?
​

A) 0.45
B) 1.00 (i.e. ,no change)
C) 2.24
D) 5.00
E) 4.47

Question 63

A 2-m long piano string of mass 10 g is under a tension of 348 N.Find the speed with which a wave travels on this string.
​

A) 528 m/s
B) 264 m/s
C) 132 m/s
D) 373 m/s
E) ​83 m/s

Question 64

A wave travels in a string at 64 m/s.A second string of 25% greater linear density has the same tension applied as in the first string.What will be the resulting wave speed in the second string?
​

A) also 64 m/s
B) 74 m/s
C) 128 m/s
D) 57 m/s
E) ​72 m/s

Question 65

For a wave traveling in a string,by what factor would the tension need to be increased to quinary the wave speed?
​

A) 2.2
B) 5
C) 25
D) 125
E) 625

Question 66

Equal wavelength waves of amplitude 0.24 m and 0.16 m interfere with one another.What is the resulting minimum amplitude that can result?
​

A) 0.16 m
B) 0.08 m
C) 0 m
D) −0.4 m
E) 0.20 m

Question 67

Bats can detect small objects such as insects that are of a size approximately that of one wavelength.If bats emit a chirp at a frequency of 60 kHz,and the speed of sound waves in air is 340 m/s,what is the smallest size insect they can detect?
​

A) 4.7 mm
B) 3.7 mm
C) 5.7 mm
D) 6.7 mm
E) ​7.7 mm

Question 68

What is the phase difference when two waves,traveling in the same medium,undergo constructive interference?

A) 270°
B) 180°
C) 90°
D) 0°

Question 69

A wave is traveling in a string at 68 m/s.When the tension is then increased 15%,what will be the resulting wave speed?
​

A) also 68 m/s
B) 73 m/s
C) 63 m/s
D) 26 m/s
E) ​78 m/s

Question 70

Two water waves meet at the same point,one having a displacement above equilibrium of 30 cm and the other having a displacement above equilibrium of 90 cm.At this moment,what is the resulting displacement above equilibrium?

A) 120 cm
B) 75 cm.
C) 60 cm
D) Information about the amplitudes needs to be given to find an answer.
E) 75 cm

Question 71

A string is strung horizontally with a fixed tension.A wave of frequency 90 Hz is sent along the string,and it has a wave speed of 55.1 m/s.Then a second wave,one of frequency 180 Hz,is sent along the string.What is the wave speed of the second wave?
​

A) 27.6 m/s
B) 55.1 m/s
C) 110.2 m/s
D) 82.7 m/s
E) 220.4 m/s

Question 72

Waves propagate at 6.8 m/s along a stretched string.The end of the string is vibrated up and down once every 2.5 s.What is the wavelength of the waves that travel along the string?
​

A) 5 m
B) 17 m
C) 2.7 m
D) 1.9 m
E) 9.6 m

Question 73

A long string is pulled so that the tension in it increases by a factor of four.If the change in length is negligible,by what factor does the wave speed change?
​

A) 4.0
B) 2
C) 0.5
D) 0.25
E) 0.71

Question 74

The superposition principle has to do with which of the following?

A) effects of waves at great distances
B) the ability of some waves to move very far
C) how displacements of interacting waves add together
D) relativistic wave behavior

Question 75

Consider two identical and symmetrical wave pulses on a string.Suppose the first pulse reaches the fixed end of the string and is reflected back and then meets the second pulse.When the two pulses overlap exactly,the superposition principle predicts that the amplitude of the resultant pulses,at that moment,will be what factor times the amplitude of one of the original pulses?

A) 0
B) 1
C) 2
D) 4

Question 76

Transverse waves travel with a speed of 100 m/s along a taut copper wire that has a diameter of 1.73 mm.What is the tension in the wire? (The density of copper is 8.93 g/cm³. )
​

A) 839 N
B) 419 N
C) 210 N
D) 105 N
E) 67 N

Question 77

If a wave pulse is reflected from a free boundary,which of the following choices best describes what happens to the reflected pulse?

A) becomes inverted
B) remains upright
C) halved in amplitude
D) doubled in amplitude

Question 78

An earthquake emits both P-waves and S-waves that travel at different speeds through the Earth.A P-wave travels at 9,000 m/s and an S-wave at 4,000 m/s.If P-waves are received at a seismic station 44.2 s before an S-wave arrives,how far is the station from the earthquake center?
​

A) 159 km
B) 636 km
C) 318 km
D) 122 km
E) ​2,210 km

Question 79

If a long spring with spring constant k is cut into 4 equal lengths,what is the spring constant of each of the 4 shorter springs?
​

A) It is still k.
B) It is k/4.
C) It is 4k.
D) It is k/16.
E) ​It is k + 4.

Question 80

A mass-spring system on a horizontal frictionless surface is set in simple harmonic motion with amplitude A.The mass is then doubled and the system is again set into simple harmonic motion with the same amplitude.Which of the following is true about the total mechanical energy of the system due to doubling the mass?

A) It has doubled.
B) It has quadrupled.
C) It has halved.
D) It has not changed.