Deck 13: Vibrations and Waves

Question 1

If it takes 7 N to stretch a spring 8 cm and if the spring is then cut in half,what force does it take to stretch one of the halves 4 cm?​

A)3.5 N
B)7 N
C)14 N
D)21 N
E)​28 N

Answer 1

7 N

Question 2

A 0.30-kg object is oscillating on a spring with a spring constant of k = 22.0 N/m.What is the potential energy of the system when the object displacement is 0.035 m,exactly half the maximum amplitude?

A)zero
B)0.027 J
C)0.013 J
D)0.39 J
E)11 J

Answer 2

0.013 J

Question 3

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.

Answer 3

A ball bouncing on the floor.

Question 4

Spring #1 has spring constant 61.0 N/m.Spring #2 has an unknown spring constant,but when connected in series with Spring #1,the connected springs have an effective spring constant of 20.0 N/m.What is the spring constant for Spring #2?

A)41.0 N/m
B)81.0 N/m
C)15.1 N/m
D)29.8 N/m
E)71.0 N/m

Question 5

Doubling 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)0.50
B)1.0
C)2.0
D)4.0
E)0.25

Question 6

A mass of 0.40 kg,attached to a spring with a spring constant of 40 N/m,is set into simple harmonic motion.What is the magnitude of the acceleration of the mass when at its maximum displacement of 0.25 m from the equilibrium position?

A)zero
B)13 m/s²
C)6.3 m/s²
D)25 m/s²
E)50 m/s²

Question 7

A large spring requires a force of 130 N to compress it only 0.01 m.What is the spring constant of the spring?

A)13 N/m
B)13 000 N/m
C)1.3 N/m
D)130 N/m
E)6 500 N/m

Question 8

A 0.400-kg object is attached to a spring with spring constant k = 10.0 N/m and moves with simple harmonic motion over a horizontal frictionless surface.At the instant that it is displaced from equilibrium by −0.0550 m,what is its acceleration?

A)2 200 m/s²
B)−220 m/s²
C)0.220 m/s²
D)1.38 m/s²
E)0.550 m/s²

Question 9

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

A)kg⋅s²
B)kg/m²
C)kg/s²
D)kg⋅m²

Question 10

A 0.200-kg object,attached to a spring with spring constant k = 16.0 N/m,is moving on a horizontal frictionless surface in simple harmonic motion of amplitude of 0.0840 m.What is its speed at the instant when its displacement is 0.0420 m? (Hint: Use conservation of energy. )

A)6.51 m/s
B)0.269 m/s
C)65.1 cm/s
D)84.0 cm/s
E)46.0 cm/s

Question 11

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)3k
C)k/3
D)1.73k

Question 12

A tiny spring,with a spring constant of 1.30 N/m,will be stretched to what displacement by a 0.00500-N force?

A)3.85 mm
B)7.69 mm
C)11.5 mm
D)6.50 mm
E)3.25 mm

Question 13

A mass of 0.40 kg,hanging from a spring with a spring constant of 75.0 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 0.20 m.

A)zero
B)2.7 m/s
C)3.9 m/s
D)3.4 m/s
E)0.55 m/s

Question 14

A mass of 4.5 kg,resting on a horizontal frictionless surface,is attached on the right to a horizontal spring with spring constant 29 N/m and on the left to a horizontal spring with spring constant 60 N/m.If this system is moved from equilibrium,what is the effective spring constant?

A)-31 N/m
B)31 N/m
C)89 N/m
D)-89 N/m
E)16 N/m

Question 15

Two springs,each with spring constant 33.0 N/m,are connected in parallel,and the combination is hung vertically from one end.A 18.0-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)0.545 m
B)0.136 m
C)1.09 m
D)0.273 m
E)2.18 m

Question 16

A mass of 0.40 kg,hanging from a spring with a spring constant of 82 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 0.10 m from its equilibrium position.

A)zero
B)0.36 m/s
C)0.11 m/s
D)1.6 m/s
E)0.72 m/s

Question 17

Tripling 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)0.33
B)1.0
C)3.0
D)9.0
E)0.11

Question 18

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

Question 19

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 20

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 21

A 0.30-kg block rests on a frictionless level surface and is attached to a horizontally aligned spring with a spring constant of 52.0 N/m.The block is initially displaced 3.20 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)2.36 m/s
B)0.596 m/s
C)1.67 m/s
D)0.421 m/s
E)2.28 m/s

Question 22

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 23

If a simple harmonic motion is described by x = 3 cos(πt),starting from t = 0 s,what is the first occurrence of a value of t for which x = 0? Assume SI units.

A)t = 0 s
B)t = s
C)t = s
D)t = s

Question 24

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.

Question 25

An ore car of mass 4 900 kg rolls downhill on tracks from a mine.At the end of the tracks,13.5 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)1.26 m
B)0.889 m
C)1.78 m
D)0.568 m
E)0.484 m

Question 26

Suppose a 0.70-kg mass on a spring that has been compressed 0.26 m has elastic potential energy of 2.20 J.How much further must the spring be compressed to triple the elastic potential energy?

A)0.45 m
B)0.71 m
C)0.78 m
D)0.19 m
E)0.52 m

Question 27

A mass on a spring vibrates in simple harmonic motion at a frequency of 4.20 Hz and an amplitude of 7.50 cm.If the mass of the object is 0.260 kg,what is the spring constant?

A)6.86 N/m
B)696 N/m
C)181 N/m
D)24.1 N/m
E)339 N/m

Question 28

A car with bad shocks bounces up and down with a period of 1.51 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)6.9E+3 N/m
B)1.7E+3 N/m
C)1.7E+3 N/m.
D)3.5E+3 N/m
E)8.2E+2 N/m

Question 29

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 86 N/m,then what is the amplitude of oscillation of each oxygen atom?

A)3.2E-11 m
B)1.6E-11 m
C)1.1E-11 m
D)6.1E-12 m
E)4.3E-12 m

Question 30

A 0.38-kg block rests on a level surface and is attached to a horizontally aligned spring with a spring constant of 55.0 N/m.The block is initially displaced 4.8 cm from the equilibrium point and then released to set up a simple harmonic motion.A frictional force of 0.50 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 4.8-cm displacement point?

A)0.21 m/s
B)0.32 m/s
C)0.64 m/s
D)0.46 m/s
E)1.8 m/s

Question 31

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 four times the original value.By what factor is the frequency of oscillation changed?

A)1/4
B)1/
C)1/16
D)4
E)16

Question 32

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

A)1/25
B)1/5
C)5
D)25
E)1

Question 33

When an object is moving in simple harmonic motion,which of the following is at a minimum when the displacement from equilibrium is zero?

A)the magnitude of the velocity
B)the magnitude of the acceleration
C)the kinetic energy
D)the total mechanical energy

Question 34

A runaway railroad car,with mass 45.0 × 10⁴ kg,coasts across a level track at 3.80 m/s when it collides with a spring-loaded bumper at the end of the track.If the spring constant of the bumper is 3.80 × 10⁶ N/m,what is the maximum compression of the spring during the collision? (Assume the collision is elastic. )

A)1.31 m
B)1.85 m
C)0.925 m
D)2.10 m
E)2.62 m

Question 35

A 0.20-kg mass is oscillating on a spring over a horizontal frictionless surface.When it is at a displacement of 2.3 cm for equilibrium it has a kinetic energy of 1.5 J and a spring potential energy of 2.3 J.What is the maximum speed of the mass during its oscillation?

A)4.4 m/s
B)0.16 m/s
C)6.2 m/s
D)4.8 m/s
E)3.0 m/s

Question 36

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 37

I attach a 4.0-kg block to a spring that obeys Hooke's law and supply 3.4 J of energy to stretch the spring.I release the block;it oscillates with period 0.15 s.The amplitude is

A)2.2 cm.
B)3.1 cm.
C)1.6 cm.
D)20 cm.
E)4.4 cm.

Question 38

Suppose a 0.74-kg mass on a spring that has been compressed 0.100 m has elastic potential energy of 1.20 J.What is the spring constant?

A)178 N/m
B)320 N/m
C)240 N/m
D)24.0 N/m
E)74.0 N/m

Question 39

Two identical springs,each with spring constant k,are attached in parallel to a mass,which is then set into simple harmonic motion.What would be the spring constant of a single spring which would result in the same frequency of oscillation as the parallel springs?

A)k
B)2k
C)k/2
D)

Question 40

Suppose a 0.45-kg mass on a spring-loaded gun that has been compressed 0.10 m has elastic potential energy of 1.50 J.How high above the spring's equilibrium point can the gun fire the mass if the gun is fired straight up?

A)0.34 m
B)0.58 m
C)0.24 m
D)3.2 m
E)33 m

Question 41

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 42

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 43

A simple pendulum has a period of 4.40 s.What is the pendulum length? (g = 9.80 m/s²)

A)19.2 m
B)15.1 m
C)4.81 m
D)0.208 m
E)0.0520 m

Question 44

An object moving in simple harmonic motion has an amplitude of 0.0450 m and a maximum acceleration of 40.0 m/s².What is the frequency of the system?

A)14.9 Hz
B)187 Hz
C)4.75 Hz
D)11.9 Hz
E)1.80 Hz

Question 45

The wave-related quantity algebraically equivalent to 1/f is

A)ω
B)T
C)A
D)λ

Question 46

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 47

A mass on a spring vibrates in simple harmonic motion at a frequency of 4.26 Hz and an amplitude of 3.00 cm.If a timer is started when its displacement is a maximum (hence x = 3.00 cm when t = 0),what is the acceleration magnitude when t = 3.74 s?

A)zero
B)0.732 m/s²
C)39.2 m/s²
D)19.6 m/s²
E)10.5 m/s²

Question 48

The position of a 0.76-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)4.7E-3 N
B)2.9E-2 N
C)6.2E-3 N
D)2.4E-2 N
E)​2.4E-2 N

Question 49

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

A)1/3
B)1
C)3²
D)3
E)1/3²

Question 50

A mass on a spring vibrates in simple harmonic motion at a frequency of 3.2 Hz and an amplitude of 6.4 cm.If a timer is started when its displacement is a maximum (hence x = 6.4 cm when t = 0),what is the displacement of the mass when t = 3.3 s?

A)zero
B)-5.95 cm
C)-2.36 cm
D)2.53 cm

Question 51

A mass on a spring vibrates in simple harmonic motion at a frequency of 8.0 Hz and an amplitude of 2.0 cm.If a timer is started when its displacement is a maximum (hence x = 2.0 cm when t = 0),what is the speed of the mass when t = 3.0 s?

A)zero
B)100 m/s
C)3.0 m/s
D)2.0 m/s
E)50 m/s

Question 52

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 15.6 cm,what is its maximum speed when the engine is running at 3 480 rpm?

A)28.4 m/s
B)14.2 m/s
C)56.9 m/s
D)7.11 m/s
E)3.55 m/s

Question 53

​A block on a level,frictionless surface and connected to a spring undergoes simple harmonic motion with amplitude A.At x = 0,which relationship is correct?

A)​|v| < |v_max|
B)​|v| = |v_max|
C)​|v| > |v_max|
D)​Not enough information to determine a relationship.

Question 54

The position of a 0.700-kg mass undergoing simple harmonic motion is given by x = (0.160 m)cos (πt/16).What is its position at t = 5.80 s?

A)-0.0670 m
B)0.0622 m
C)6.25 m
D)0.0670 m
E)0.610 m

Question 55

A simple pendulum has a mass of 0.202 kg and a length of 1.00 m.It is displaced through an angle of 31.4° and then released.After a time,the maximum angle of swing is only 10.0°.How much energy has been lost to friction?

A)0.260 J
B)0.290 J
C)0.0301 J
D)1.00 J
E)0.320 J

Question 56

By what factor should the length of a simple pendulum be changed if the period of vibration were to be increased by a factor of three?

A)1/3²
B)1/3
C)3
D)3²
E)1

Question 57

The position of a 0.64-kg mass undergoing simple harmonic motion is given by x = (0.160 m)cos (πt/16).What is its period of oscillation?

A)100 s
B)32 s
C)16 s
D)8.0 s
E)4.0 s

Question 58

A pendulum on the Earth has a period T.The acceleration of due to gravity on Mars is less than that on the Earth,and the acceleration due to gravity on the Moon is even less.Where would the period of an identical pendulum be the least?

A)on the Earth
B)on the Moon
C)on Mars
D)The period of a pendulum would be the same on the Earth,Moon,and Mars since the period depends on the pendulum's length which is the same for identical pendula.

Question 59

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 60

A simple pendulum of length 1.87 m has a mass of 120 g attached.It is drawn back 38.0° and then released.What is the maximum speed of the mass?

A)1.44 m/s
B)3.93 m/s
C)2.74 m/s
D)2.79 m/s
E)0.249 m/s

Question 61

If you quadruple the mass per unit length of a guitar string the wave speed in the string will change by what factor?

A)
B)
C)
D)4.00

Question 62

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 63

A traveling wave train has wavelength 0.400 m,speed 35.0 m/s.Find the wave frequency.

A)0.0114 Hz
B)43.8 Hz
C)87.5 Hz
D)21.9 Hz
E)55.3 Hz

Question 64

If a radio wave has speed 3.00 × 10⁸ m/s and frequency 94.3 MHz,what is its wavelength?

A)1.59 m
B)2.14 m
C)4.24 m
D)3.18 m
E)6.30 m

Question 65

Triple 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)
B)1 (i.e. ,no change)
C)
D)3
E)2

Question 66

Transverse waves travel with a speed of 105 m/s along a taut copper wire that has a diameter of 2.28 mm.What is the tension in the wire? (The density of copper is 8.93 g/cm³. )

A)1 610 N
B)803 N
C)402 N
D)201 N
E)128 N

Question 67

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 68

Sound waves of a certain frequency in air having a wavelength of 1.9 m will have what wavelength in water? Take the speed of sound in air to be 340 m/s and in water to be 1 490 m/s.

A)0.57 m
B)1.9 m
C)8.3 m
D)11 m

Question 69

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

A)
B)4
C)4²
D)4³
E)4⁴

Question 70

A water bug on the surface of a pond bobs up and down three times per second on ripples with wavelength 10.5 cm.A fish resting at the surface of the pond is 8.50 m from the water bug.How long does it take a ripple passing the water bug to reach the fish?

A)27.0 s
B)243 s
C)81.0 s
D)0.893 s

Question 71

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 34.0 s before an S-wave arrives,how far is the station from the earthquake center?

A)1.22E+5 m
B)4.90E+5 m
C)2.45E+5 m
D)9.42E+4 m
E)1.70E+5 m

Question 72

A musical tone,sounded on a piano,has a frequency of 460 Hz and a wavelength in air of 0.50 m.What is the wave speed?

A)920 m/s
B)270 m/s
C)230 m/s
D)109 m/s
E)115 m/s

Question 73

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 74

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
B)
C)
D)
E)

Question 75

A 2.00-m long piano string of mass 10.0 g is under a tension of 320 N.Find the speed with which a wave travels on this string.

A)506 m/s
B)253 m/s
C)126 m/s
D)358 m/s
E)80.0 m/s

Question 76

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 77

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 335 m/s,what is the smallest size insect they can detect?

A)4.6 mm
B)3.6 mm
C)5.6 mm
D)6.6 mm
E)7.6 mm

Question 78

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 79

Waves propagate at 7.40 m/s along a stretched string.The end of the string is vibrated up and down once every 2.25 s.What is the wavelength of the waves that travel along the string?

A)4.50 m
B)16.7 m
C)3.29 m
D)37.5 m
E)8.09 m

Question 80

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

A)270°
B)180°
C)90°
D)0°