JEE Physics Waves MCQs Set 29

Practice MCQs for JEE Physics Waves

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Multiple Choice Questions

Question 1: A pebble is dropped in a pond of still water and disturbs the water surface. Which of the given statements are correct? I. The disturbance produced does not remain confined to one place but propagates outward along a circle. II. If a cork piece is put on the disturbed surface, it moves along with the disturbance in the same direction. III. The water mass does not flow outward with the circles formed but rather a moving disturbance is created.
(a) I and III
(b) II and III
(c) I, II and III
(d) I and II
Show Answer & Explanation

Answer: (a) I and III

Explanation:
1. The ripples spread outward (I) and no bulk water moves with them (III).
2. A cork only bobs up and down and does not move outward, so II is false.

Teacher's Note:
1. Waves move, medium does not.

Question 2: Beats are the result of
(a) diffraction
(b) destructive interference
(c) constructive and destructive interference
(d) superposition of two waves of nearly equal frequency
Show Answer & Explanation

Answer: (d) superposition of two waves of nearly equal frequency

Explanation:
1. Beats arise when two waves of slightly different frequencies are superposed.
2. The amplitude then rises and falls periodically.

Teacher's Note:
1. Beat frequency = f₁ − f₂.

Question 3:
Assertion (A): Particle velocity and wave velocity are both independent of time.
Reason (R): For the propagation of wave motion, the medium must have the properties of elasticity and inertia.
(a) Both A and R are true, and R is the correct explanation of A.
(b) Both A and R are true, but R is not the correct explanation of A.
(c) A is true, but R is false.
(d) A is false, but R is true.
Show Answer & Explanation

Answer: (d) A is false, but R is true.

Explanation:
1. The wave velocity is constant but the particle velocity changes with time, so the assertion is false.
2. The reason is a true statement.

Teacher's Note:
1. Particle velocity is periodic.

Question 4: Tube A has both ends open while tube B has one end closed, otherwise they are identical. The ratio of the fundamental frequencies of tubes A and B is
(a) 1 : 2
(b) 1 : 4
(c) 2 : 1
(d) 4 : 1
Show Answer & Explanation

Answer: (c) 2 : 1

Explanation:
1. f_A = v/2L and f_B = v/4L.
2. The ratio is 2 : 1.

Teacher's Note:
1. Open: v/2L; closed: v/4L.

Question 5: Sound travels in rocks in the form of
(a) longitudinal elastic waves only
(b) transverse elastic waves only
(c) both longitudinal and transverse elastic waves
(d) non-elastic waves
Show Answer & Explanation

Answer: (c) both longitudinal and transverse elastic waves

Explanation:
1. Solids have both bulk and shear moduli.
2. So both longitudinal and transverse waves can travel.

Teacher's Note:
1. Solids support both types.

Question 6: Match Column I with Column II.
Column IColumn II
(A) A region of low pressure and low density(1) Particles oscillate at right angle to the direction of propagation
(B) A region of high pressure and high density(2) Particles oscillate in the same direction as propagation
(C) Longitudinal wave(3) Compression
(D) Transverse wave(4) Rarefaction

(a) A-4, B-2, C-3, D-1
(b) A-3, B-4, C-2, D-1
(c) A-4, B-3, C-2, D-1
(d) A-4, B-1, C-2, D-3
Show Answer & Explanation

Answer: (c) A-4, B-3, C-2, D-1

Explanation:
1. Low pressure and density is a rarefaction (A-4).
2. High pressure and density is a compression (B-3).
3. In a longitudinal wave the particles oscillate along the direction of propagation (C-2).
4. In a transverse wave they oscillate at right angles (D-1).

Teacher's Note:
1. Compressions and rarefactions.

Question 7: A wave travelling in the +x direction has a displacement along y of 1 m, a wavelength 2π m and a frequency 1/π Hz. It is represented by
(a) \( y=\sin(2\pi x-2\pi t) \)
(b) \( y=\sin(10\pi x-20\pi t) \)
(c) \( y=\sin(2\pi x+2\pi t) \)
(d) \( y=\sin(x-2t) \)
Show Answer & Explanation

Answer: (d) \( y=\sin(x-2t) \)

Explanation:
1. k = 2π/λ = 1 rad/m and ω = 2πf = 2 rad/s.
2. A wave in the +x direction is y = sin(kx − ωt) = sin(x − 2t).

Teacher's Note:
1. Find k and ω.

Question 8: Which of the following statements are correct? I. A steel bar possesses both bulk and shear elastic moduli. II. A steel bar propagates both longitudinal as well as transverse waves having different speeds. III. Air can propagate both longitudinal and transverse waves.
(a) I and III
(b) II and III
(c) I and II
(d) I, II and III
Show Answer & Explanation

Answer: (c) I and II

Explanation:
1. Steel has both moduli and carries longitudinal and transverse waves at different speeds.
2. Air has no shear modulus and carries only longitudinal waves, so III is false.

Teacher's Note:
1. Fluids lack shear modulus.

Question 9:
Assertion (A): Two waves moving in a uniform string having uniform tension cannot have different velocities.
Reason (R): The elastic and inertial properties of the string are the same for all waves in the same string. Moreover, the speed of a wave in a string depends on its elastic and inertial properties only.
(a) Both A and R are true, and R is the correct explanation of A.
(b) Both A and R are true, but R is not the correct explanation of A.
(c) A is true, but R is false.
(d) A is false, but R is true.
Show Answer & Explanation

Answer: (a) Both A and R are true, and R is the correct explanation of A.

Explanation:
1. v = √(T/μ) depends only on the tension and the mass per unit length.
2. These are the same for both waves, so their speeds are equal.

Teacher's Note:
1. Speed depends on the medium only.

Question 10: A string is stretched between two fixed points separated by 75.0 cm. It is observed to have resonant frequencies of 420 Hz and 315 Hz, with no other resonant frequencies between these two. The lowest resonant frequency for this string is
(a) 205 Hz
(b) 10.5 Hz
(c) 105 Hz
(d) 155 Hz
Show Answer & Explanation

Answer: (c) 105 Hz

Explanation:
1. Consecutive harmonics differ by the fundamental frequency.
2. f₁ = 420 − 315 = 105 Hz.

Teacher's Note:
1. Harmonics are n f₁.

Question 11: The Doppler shift in frequency does not depend upon
(a) the frequency of the wave produced
(b) the velocity of the source
(c) the velocity of the observer
(d) the distance from the source to the listener
Show Answer & Explanation

Answer: (d) the distance from the source to the listener

Explanation:
1. f′ depends on f, v_s and v_o.
2. The distance between source and listener does not enter.

Teacher's Note:
1. No distance in the formula.

Question 12: Match Column I with Column II.
Column IColumn II
(A) Pitch(1) Waveform
(B) Quality(2) Frequency
(C) Loudness(3) Intensity
(D) Nodes(4) Position of zero amplitude

(a) A-3, B-1, C-2, D-4
(b) A-2, B-4, C-3, D-1
(c) A-1, B-2, C-3, D-4
(d) A-2, B-1, C-3, D-4
Show Answer & Explanation

Answer: (d) A-2, B-1, C-3, D-4

Explanation:
1. Pitch is related to frequency (A-2).
2. Quality (timbre) depends on the waveform (B-1).
3. Loudness depends on intensity (C-3).
4. Nodes are points of zero amplitude (D-4).

Teacher's Note:
1. Characteristics of sound.

Question 13: Shock waves are produced by objects
(a) carrying electric charge and vibrating
(b) vibrating with a frequency greater than 20000 Hz
(c) vibrating with a very large amplitude
(d) moving with a speed greater than that of sound in the medium
Show Answer & Explanation

Answer: (d) moving with a speed greater than that of sound in the medium

Explanation:
1. A source moving faster than sound produces a conical shock wave.

Teacher's Note:
1. Supersonic motion.

Question 14: Of the following, the equation of a plane progressive wave is
(a) \( y=r\sin\omega t \)
(b) \( y=r\sin(\omega t-kx) \)
(c) \( y=\frac{a}{\sqrt r}\sin(\omega t-kx) \)
(d) \( y=\frac ar\sin(\omega t-kr) \)
Show Answer & Explanation

Answer: (b) \( y=r\sin(\omega t-kx) \)

Explanation:
1. A plane wave has a constant amplitude and travels along one direction.
2. y = r sin(ωt − kx) is of this form; the others are not plane waves.

Teacher's Note:
1. Plane wave: constant amplitude.

Question 15: A travelling wave reflected at an open boundary undergoes a phase change of
(a) \( \pi \)
(b) 0
(c) \( \pi/2 \)
(d) \( \pi/3 \)
Show Answer & Explanation

Answer: (b) 0

Explanation:
1. An open (free) boundary reflects the wave with no phase change.

Teacher's Note:
1. Open end: 0.

Question 16: If n₁, n₂ and n₃ are the fundamental frequencies of three segments into which a string is divided, then the original fundamental frequency n of the string is given by
(a) \( \frac1n=\frac1{n_1}+\frac1{n_2}+\frac1{n_3} \)
(b) \( \frac1{\sqrt n}=\frac1{\sqrt{n_1}}+\frac1{\sqrt{n_2}}+\frac1{\sqrt{n_3}} \)
(c) \( \sqrt n=\sqrt{n_1}+\sqrt{n_2}+\sqrt{n_3} \)
(d) \( n=n_1+n_2+n_3 \)
Show Answer & Explanation

Answer: (a) \( \frac1n=\frac1{n_1}+\frac1{n_2}+\frac1{n_3} \)

Explanation:
1. At fixed tension and mass per length, n ∝ 1/L.
2. Since L = L₁ + L₂ + L₃, 1/n = 1/n₁ + 1/n₂ + 1/n₃.

Teacher's Note:
1. n ∝ 1/L.

Question 17: A whistle producing sound waves of frequency 9500 Hz and above is approaching a stationary person with speed v m/s. The velocity of sound in air is 300 m/s. If the person can hear frequencies up to a maximum of 10,000 Hz, the maximum value of v up to which he can hear the whistle is
(a) \( 15\sqrt2\ \text{m/s} \)
(b) \( \frac{15}{\sqrt2}\ \text{m/s} \)
(c) \( 15\ \text{m/s} \)
(d) \( 30\ \text{m/s} \)
Show Answer & Explanation

Answer: (c) \( 15\ \text{m/s} \)

Explanation:
1. f′ = 9500 × 300/(300 − v) ≤ 10000.
2. So 300 − v ≥ 285 and v ≤ 15 m/s.

Teacher's Note:
1. Doppler for an approaching source.

Question 18: Phon is the unit of
(a) wavelength
(b) loudness
(c) frequency
(d) intensity
Show Answer & Explanation

Answer: (b) loudness

Explanation:
1. The phon is a unit of loudness level.

Teacher's Note:
1. Phon measures loudness.

Question 19: Frequencies of sound produced from an organ pipe open at both ends are
(a) only the fundamental note
(b) only even harmonics
(c) only odd harmonics
(d) even and odd harmonics
Show Answer & Explanation

Answer: (d) even and odd harmonics

Explanation:
1. An open pipe produces f, 2f, 3f, ….
2. So both even and odd harmonics are present.

Teacher's Note:
1. All harmonics.

Question 20: When a wave is reflected from a denser medium, the change in phase is
(a) 0
(b) \( \pi \)
(c) \( 2\pi \)
(d) \( 3\pi \)
Show Answer & Explanation

Answer: (b) \( \pi \)

Explanation:
1. Reflection at a denser medium (fixed end) reverses the displacement.
2. This is a phase change of π.

Teacher's Note:
1. Denser medium: phase change π.

Question 21: For which of the following cases will there be no Doppler effect?
(a) If the source and the listener both move in the same direction with the same speed
(b) If one of the source/listener is at the centre of a circle while the other is moving on it
(c) When both the source and the listener are at rest
(d) all of these
Show Answer & Explanation

Answer: (d) all of these

Explanation:
1. The Doppler effect needs relative motion along the line joining source and listener.
2. There is none in any of the three cases.

Teacher's Note:
1. No relative radial motion, no shift.

Question 22: A progressive wave y = A sin(kx − ωt) is reflected by a rigid wall at x = 0. Then the reflected wave can be represented by
(a) \( y=A\sin(kx+\omega t) \)
(b) \( y=A\cos(kx+\omega t) \)
(c) \( y=-A\sin(kx-\omega t) \)
(d) \( y=-A\sin(kx+\omega t) \)
Show Answer & Explanation

Answer: (a) \( y=A\sin(kx+\omega t) \)

Explanation:
1. The reflected wave travels in the −x direction and has a phase change of π: y_r = −A sin(−kx − ωt) = A sin(kx + ωt).
2. At x = 0 the total displacement −A sin ωt + A sin ωt = 0, as required at a rigid wall.

Teacher's Note:
1. Boundary condition y = 0 at x = 0.

Question 23: The tenth harmonic is set up in a pipe. The pipe is
(a) an open pipe
(b) a closed pipe
(c) any of them
(d) none
Show Answer & Explanation

Answer: (a) an open pipe

Explanation:
1. A closed pipe produces only odd harmonics.
2. The tenth (even) harmonic can only appear in an open pipe.

Teacher's Note:
1. Even harmonics need an open pipe.

Question 24: A sinusoidal travelling wave is described by y(x, t) = a sin(kx − ωt + φ). The value of the displacement will
(a) vary from 0 to a
(b) vary from 0 to −a
(c) vary from −a to a
(d) none of these
Show Answer & Explanation

Answer: (c) vary from −a to a

Explanation:
1. The sine function takes all values between −1 and 1.
2. The displacement therefore varies from −a to a.

Teacher's Note:
1. Range of sine.

Question 25: Choose the false statement(s) about the speed of transverse waves on a stretched string. I. It depends on the linear mass density of the string. II. It depends on the tension in the string. III. It depends on the frequency of the wave.
(a) I only
(b) II only
(c) III only
(d) I, II and III
Show Answer & Explanation

Answer: (c) III only

Explanation:
1. v = √(T/μ) depends on tension and linear mass density only.
2. It does not depend on the frequency.

Teacher's Note:
1. v = √(T/μ).

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