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Wave Motion and Waves on a String — JEE Main & Advanced Physics PYQs

128 previous year questions from Wave Motion and Waves on a String with answers and solutions. Numbered list, year tags, and one-tap solutions — built for serious JEE / NEET practice.

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1

A wave pulse travelling on a string at a speed of 40 cm s ⁻¹ in the negative x -direction has its maximum located at x = 0 when t = 0 . Where will this maximum be found at t = 5 s

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2

A wave travelling on a string stretched along the X -axis has an equation given by y = A , e^ - ( x a + t T )^2 . Identify the direction in which the wave is travelling.

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3

A wave travelling on a string stretched along the X -axis has an equation given by y = A , e^ - ( x a + t T )^2 . Locate the maximum of the pulse at t = T and at t = 2T respectivel

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4

A wave travelling on a string stretched along the X -axis has an equation given by y = A , e^ - ( x a + t T )^2 . Determine the dimensions of A , a , and T .

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5

A wave travelling on a string stretched along the X -axis has an equation given by y = A , e^ - ( x a + t T )^2 . Compute the wave speed.

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6

A stretched string carries a wave in the positive x -direction with a wave speed of v . The displacement of the particle at x = 0 is described by f(t) = A (t/T) . Determine the wav

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7

A pulse travelling on a string is described by the function y = a^3 (x - vt)^2 + a^2 , where a = 5 mm and v = 20 cm s ⁻¹ . Taking x = 0 at the middle of the string, determine the p

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8

The figure displays a wave pulse at t = 0 . The pulse travels to the right with a speed of 10 cm s ⁻¹ . Determine the respective rightward shifts of the shape of the string at t =

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9

A wave pulse travels on a string towards the positive X -axis with a speed v . At t = 0 , the shape of the string is given by g(x) = A (x/a) , where A and a are constants. Write th

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10

A wave pulse travels on a string towards the positive X -axis with a speed v . At t = 0 , the shape of the string is given by g(x) = A (x/a) , where A and a are constants. Determin

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11

A wave travels on a string in the positive x -direction at a velocity v . The shape of the string at t = t₀ is described by g(x, t₀) = A (x/a) . Determine the wave equation for a g

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12

A wave travelling on a string has the equation y = (0.10 mm ) [(31.4 m ⁻¹)x + (314 s ⁻¹)t] . In which direction does the wave travel?

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13

A wave travelling on a string has the equation y = (0.10 mm ) [(31.4 m ⁻¹)x + (314 s ⁻¹)t] . Determine the wave speed, the wavelength and the frequency of the wave.

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14

A wave travelling on a string has the equation y = (0.10 mm ) [(31.4 m ⁻¹)x + (314 s ⁻¹)t] . What is the maximum displacement and the maximum speed of a portion of the string?

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15

A wave propagates along the positive x -direction with a speed of 20 m s ⁻¹ . The amplitude of the wave is 0.20 cm and the wavelength is 2.0 cm . Which of the following is a possib

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16

A wave travels along the positive x -direction with a speed of 20 m s ⁻¹ . The amplitude of the wave is 0.20 cm and the wavelength is 2.0 cm . Assuming the wave is described by the

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17

A wave is described by the equation y = (1.0 mm ) ( x 2.0 cm - t 0.01 s ) . Find the time period and the wavelength.

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18

A wave is described by the equation y = (1.0 mm ) ( x 2.0 cm - t 0.01 s ) . Find the speed of the particle at x = 1.0 cm at time t = 0.01 s .

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19

A wave is described by the equation y = (1.0 mm ) ( x 2.0 cm - t 0.01 s ) . What are the speeds of the particles at x = 3.0 cm , 5.0 cm and 7.0 cm at t = 0.01 s ?

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20

A wave is described by the equation y = (1.0 mm ) ( x 2.0 cm - t 0.01 s ) . What are the speeds of the particles at x = 1.0 cm at t = 0.011 , 0.012 , and 0.013 s ?

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21

A particle on a stretched string supporting a travelling wave takes 5.0 ms to travel from its mean position to the extreme position. The distance separating two consecutive particl

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22

A travelling wave is passing along a string in the positive x -direction with a wave speed of 20 cm s ⁻¹ . The transverse displacements of the particles of the string at t = 0 are

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23

A travelling wave is passing along a string in the positive x -direction with a wave speed of 20 cm s ⁻¹ . The transverse displacements of the particles of the string at t = 0 are

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24

A travelling wave is passing along a string in the positive x -direction with a wave speed of 20 cm s ⁻¹ . The transverse displacements of the particles of the string at t = 0 are

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25

A travelling wave is passing along a string in the positive x -direction with a wave speed of 20 cm s ⁻¹ . The transverse displacements of the particles of the string at t = 0 are

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26

A wave traveling on a string at a speed of 10 m s ⁻¹ causes each particle of the string to oscillate with a time period of 20 ms . Determine the wavelength of the wave.

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27

A wave traveling on a string at a speed of 10 m s ⁻¹ causes each particle of the string to oscillate with a time period of 20 ms . If a particle has a displacement of 1.5 mm at a s

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28

A steel wire with a length of 64 cm weighs 5 g . If it is stretched by an 8 N force, determine the speed of a transverse wave travelling on it.

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29

A string of length 20 cm and linear mass density 0.40 g cm ⁻¹ is fixed at both ends and maintained under a tension of 16 N . At t = 0 , a wave pulse is created near one end, as sho

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30

A string with a total length of 30 cm and a linear mass density of 0.5 g cm ⁻¹ is attached to a fixed wall at one end, while its other end is tied to a frictionless ring that is fr

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31

A string of total length 30 cm and linear mass density 0.5 g cm ⁻¹ is secured to a fixed wall at one end and to a frictionless ring on a vertical rod at the other end. A symmetric

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32

One end of a string having a total length of 30 cm and a linear mass density of 0.5 g cm ⁻¹ is fixed to a wall, and the other end is attached to a frictionless ring that slides on

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33

Two wires possessing different densities but the same area of cross section are joined together at one end and stretched to a tension T . The velocity of a transverse wave in the f

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34

A transverse wave given by y = (0.02 m ) [(1.0 m ⁻¹)x + (30 s ⁻¹)t] propagates along a stretched string with a linear mass density of 1.2 10⁻⁴ kg m ⁻¹ . Determine the tension in th

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35

By sinusoidally vibrating one end of a long horizontal string up and down, a travelling wave is generated. The vibration amplitude is 1.0 cm , and the displacement reaches zero 200

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36

By sinusoidally vibrating one end of a long horizontal string up and down, a travelling wave is generated. The vibration amplitude is 1.0 cm , and the displacement reaches zero 200

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37

By sinusoidally vibrating one end of a long horizontal string up and down, a travelling wave is generated. The vibration amplitude is 1.0 cm , and the displacement reaches zero 200

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38

A string of length 40 cm and weighing 10 g is connected to a spring at one end and to a fixed wall at its other end. The spring possesses a spring constant of 160 N m ⁻¹ and is str

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39

As shown in the figure, two blocks, each with a mass of 3.2 kg , are connected by a wire CD . The entire system is suspended from the ceiling using another wire AB . The linear mas

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40

For the arrangement shown in the figure, the string has a mass of 4.5 g . Calculate the time required for a transverse disturbance generated at the floor to reach the pulley. Take

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41

A 4.0 kg block is suspended from the ceiling of an elevator by a string with a linear mass density of 19.2 10⁻³ kg m ⁻¹ . Determine the speed (relative to the string) at which a wa

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42

A heavy ball hangs from the ceiling of a motor car by a light string. When the car is stationary, a transverse pulse travels on the string at a speed of 60 cm s ⁻¹ . When the car a

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43

A circular loop of string is rotating about its axis on a frictionless horizontal plane at a uniform rate, ensuring that the tangential speed of any particle of the string is v . W

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44

A heavy but uniform rope of length L is suspended from a ceiling. Determine the velocity of a transverse wave travelling on the string as a function of the distance x from the lowe

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45

A heavy but uniform rope of length L is suspended from a ceiling. If the rope is given a sudden sideways jerk at the bottom, how long will it take for the pulse to reach the ceilin

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46

A heavy but uniform rope of length L is suspended from a ceiling. A particle is dropped from the ceiling at the exact instant the bottom end of the rope is given a sudden sideways

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47

Two long strings, A and B , each possessing a linear mass density of 1.2 10⁻² kg m ⁻¹ , are stretched by tensions of 4.8 N and 7.5 N respectively. They are kept parallel to each ot

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48

A transverse wave with an amplitude of 0.50 mm and a frequency of 100 Hz is generated on a wire stretched under a tension of 100 N . Given that the wave speed is 100 m s ⁻¹ , deter

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49

A wave with a frequency of 200 Hz and an amplitude of 1 mm travels on a long string. The string has a linear mass density of 6 g m ⁻¹ and is subjected to a tension of 60 N . Determ

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50

A wave with a frequency of 200 Hz and an amplitude of 1 mm travels on a long string. The string has a linear mass density of 6 g m ⁻¹ and is subjected to a tension of 60 N . Determ

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51

A tuning fork with a frequency of 440 Hz is connected to a long string having a linear mass density of 0.01 kg m ⁻¹ and maintained under a tension of 49 N . The tuning fork generat

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52

A tuning fork with a frequency of 440 Hz is connected to a long string having a linear mass density of 0.01 kg m ⁻¹ and maintained under a tension of 49 N . The tuning fork generat

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53

A tuning fork with a frequency of 440 Hz is connected to a long string having a linear mass density of 0.01 kg m ⁻¹ and maintained under a tension of 49 N . The tuning fork generat

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54

Two waves propagating in the same direction through the same region possess equal frequencies, wavelengths, and amplitudes. If each wave has an amplitude of 4 mm and the phase diff

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55

The figure displays two wave pulses on a string at t = 0 , travelling in opposite directions with an identical wave speed of 50 cm s ⁻¹ . Among the times t = 4 ms , 6 ms , 8 ms , a

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56

Two waves, each possessing a frequency of 100 Hz , a wavelength of 2.0 cm , and an amplitude of 2.0 mm , travel in the same direction on a string. Determine the phase difference an

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57

Determine the fundamental frequency of vibration if the speed of a transverse wave on a stretched string of length 1 m is 60 m s ⁻¹ .

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58

A wire of length 2.00 m is subjected to a tension of 160 N . Determine the linear mass density of the wire if its fundamental frequency of vibration is 100 Hz .

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59

A steel wire with a mass of 4.0 g and a length of 80 cm is fixed at both its ends. The tension in the wire is 50 N . Determine the frequency and wavelength of the fourth harmonic o

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60

A piano wire weighing 6.00 g and having a length of 90.0 cm produces a fundamental frequency corresponding to "Middle C" ( = 261.63 Hz ). Determine the tension in the wire.

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61

Vibrating in its second harmonic, a sonometer wire with a length of 1.50 m between the bridges is in resonance with a tuning fork of frequency 256 Hz . Determine the speed of the t

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62

The length of the wire between the pulleys, as shown in the figure, is 1.5 m , and its mass is 12.0 g . Determine the frequency of vibration when the wire vibrates in two loops, le

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63

A stretched string of length 1 m and mass 40 g is connected to a tuning fork. The tuning fork vibrates at 128 Hz in a direction perpendicular to the string. Determine the tension r

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64

A wire fixed at both its ends is found to vibrate at resonant frequencies of 240 Hz and 320 Hz . What could be the maximum value of the fundamental frequency?

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65

A wire fixed at both its ends is found to vibrate at resonant frequencies of 240 Hz and 320 Hz . If transverse waves travel on this string at a speed of 40 m s ⁻¹ , what is the len

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66

A string fixed at both ends vibrates in a resonant mode, having a separation of 2.0 cm between consecutive nodes. In the next higher resonant frequency, the separation decreases to

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67

A string clamped at both ends is set into vibration by a 660 Hz tuning fork. The string vibrates in three loops, and the wave speed for a transverse wave on the string is 220 m s ⁻

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68

A string clamped at both ends is set into vibration by a 660 Hz tuning fork, causing it to vibrate in three loops. The wave speed for a transverse wave on the string is 220 m s ⁻¹

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69

A specific guitar wire has a length of 30.0 cm and vibrates at a frequency of 196 Hz when unobstructed. The subsequent higher notes on the scale are 220 Hz , 247 Hz , 262 Hz , and

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70

Secured at both ends, a steel wire possesses a fundamental frequency of 200 Hz . A person is capable of hearing sound up to a maximum frequency of 14 kHz . Determine the highest ha

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71

A string has three resonant frequencies at 90 Hz , 150 Hz , and 210 Hz . Determine the highest possible fundamental frequency of vibration for this string.

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72

A string exhibits three resonant frequencies at 90 Hz , 150 Hz , and 210 Hz . Identify which harmonics of the fundamental frequency these given frequencies correspond to.

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73

Three resonant frequencies of a string are measured as 90 Hz , 150 Hz , and 210 Hz . Determine which overtones these given frequencies represent.

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74

Three resonant frequencies of a string are observed to be 90 Hz , 150 Hz , and 210 Hz . If the string has a length of 80 cm , determine the speed of a transverse wave on this strin

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75

Two wires are held tight between the same pair of supports. The tensions in the wires are in the ratio 2 : 1 , their radii are in the ratio 3 : 1 , and their densities are in the r

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76

As shown in the figure, a uniform horizontal rod of length 40 cm and mass 1.2 kg is supported by two identical wires. Where must a mass of 4.8 kg be positioned on the rod such that

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77

As shown in the figure, an aluminium wire of length 60 cm is connected to a steel wire of length 80 cm , and the combination is stretched between two fixed supports, producing a te

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78

A string of length L secured at both ends vibrates in its fundamental mode with a frequency u and a maximum amplitude A . Determine the wavelength and the wave number k .

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79

A string of length L secured at both ends vibrates in its fundamental mode with a frequency and a maximum amplitude A . Choose the origin at one end of the string and the X -axis a

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80

A string, 2 m long and fixed at both ends, is set into vibrations in its first overtone. The wave speed on the string is 200 m s ⁻¹ and the amplitude is 0.5 cm . Determine the wave

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81

A string, 2 m long and fixed at both ends, is set into vibrations in its first overtone. The wave speed on the string is 200 m s ⁻¹ and the amplitude is 0.5 cm . Determine the equa

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82

A string fixed at both ends is vibrating in its third harmonic. The equation for its vibration is given by y = (0.4 cm ) [(0.314 cm ⁻¹) x] [(600 s ⁻¹)t] . Determine the frequency o

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83

A string fixed at both ends is vibrating in its third harmonic. The equation for its vibration is given by y = (0.4 cm ) [(0.314 cm ⁻¹) x] [(600 s ⁻¹)t] . Determine the positions o

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84

A string fixed at both ends is vibrating in its third harmonic. The equation for its vibration is given by y = (0.4 cm ) [(0.314 cm ⁻¹) x] [(600 s ⁻¹)t] . Determine the length of t

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85

A string fixed at both ends is vibrating in its third harmonic. The equation for its vibration is given by y = (0.4 cm ) [(0.314 cm ⁻¹) x] [(600 s ⁻¹)t] . Determine the wavelength

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86

A standing wave produced on a string fixed at both ends has the equation y = (0.4 cm ) [(0.314 cm ⁻¹) x] [(600 s ⁻¹)t] . Determine the smallest possible length of the string.

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87

A wire of length 40 cm and mass 3.2 g is stretched between two fixed supports located 40.05 cm apart. The wire vibrates at 220 Hz in its fundamental mode. Determine the Young modul

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88

As depicted in the figure, a string is stretched by a block going over a pulley. The string vibrates in its tenth harmonic in unison with a specific tuning fork. When a beaker cont

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89

A rope of length 2.00 m and mass 80 g is fixed at one end and tied to a light string at the other end. The tension in the string is 256 N . Determine the frequencies of the fundame

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90

A rope of length 2.00 m and mass 80 g is fixed at one end and tied to a light string at the other end. The tension in the string is 256 N . Determine the wavelengths corresponding

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91

A heavy string is fastened at one end to a movable support and at the other end to a light thread, as shown in the figure. The light thread passes over a fixed pulley, suspending a

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92

A sine wave propagates through a medium. What is the minimum distance between two particles that always possess the same speed?

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93

The equation y = A ^2(kx - t) characterizes a wave motion with

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94

Identify the mechanical wave from the options below.

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95

Among the following equations, which one describes a wave propagating along the Y -axis?

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96

A sine wave travels through a medium. At a specific instant, a particular particle exhibits zero displacement. The distance to the closest particle that also has zero displacement

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97

As a wave generated by a boat passes by, a cork floating in a calm pond undergoes simple harmonic motion with frequency . The frequency of the wave is

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98

Two strings A and B , constructed from the identical material, are subjected to the same tension. The radius of string A is twice the radius of string B . A transverse wave propaga

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99

As depicted in the figure, both strings are composed of the same material and share the same cross section. The pulleys are assumed to be light. If the transverse wave speed in str

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100

The velocity of sound in air is 332 m s ⁻¹ . Its velocity in a vacuum will be

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101

A wave pulse travelling along a two-piece string experiences partial transmission and partial reflection at the junction. The shape of the reflected wave is inverted relative to th

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102

The resultant wave formed by the superposition of two waves given by y = a ( t - kx) and y = a ( t - kx) has an amplitude of

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103

Two wires A and B , possessing identical geometrical construction, are stretched by a small but equal amount from their natural length. The Young's moduli of the wires are Y_A and

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104

Two wave pulses approach each other while travelling in opposite directions on a string. One pulse has a shape that is inverted relative to the other.

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105

Two periodic waves with amplitudes A₁ and A₂ travel through a region. Given that A₁ > A₂ , what is the difference between the maximum and minimum possible resultant amplitudes?

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106

Two waves having an equal amplitude A and the same frequency propagate in the same direction within a medium. The amplitude of the resultant wave is

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107

Two sine waves propagate in the same direction within a medium. Each wave possesses an amplitude of A , and the phase difference between them is 120^ . The resultant amplitude is

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108

The fundamental frequency of a vibrating string is directly proportional to the

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109

Consider two waves passing through the same string. The principle of superposition for displacement states that the net displacement of a particle on the string equals the sum of t

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110

A sonometer wire with a natural frequency of 240 Hz is made to vibrate using a tuning fork of frequency 480 Hz . The frequency at which the wire will vibrate is

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111

A sonometer wire of length l vibrates in its fundamental mode when excited by a tuning fork having a frequency of 416 Hz . If the length of the wire is doubled while keeping all ot

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112

A sonometer wire carrying a 4 kg load vibrates in its fundamental mode when excited by a tuning fork of frequency 416 Hz . If the length of the wire between the bridges is subseque

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113

A tuning fork with a frequency of 480 Hz is employed to vibrate a sonometer wire that has a natural frequency of 410 Hz . The wire will vibrate at a frequency of

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114

A mechanical wave travels in a medium along the X -axis. The particles of the medium

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115

A wave propagating through a solid

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116

A wave travelling in a gas

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117

As a transverse wave travels along the Z -axis, the particles of the medium must move

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118

A longitudinal wave is unable to

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119

When a sine wave travels through a region, two particles A and B exhibit a phase difference of .

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120

A standing wave is established on a string that is clamped at one end and free at the opposite end. The length of the string

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