JEE Physics Waves MCQs Set 27

Multiple Choice Questions (MCQs) for JEE Physics: Waves

Access targeted multiple-choice questions for Waves designed to align with the latest JEE academic syllabus for JEE Physics. These objective practice sets help students evaluate their conceptual understanding and improve exam readiness.

Practice Waves MCQs for JEE Physics

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Multiple Choice Questions

Question 1: A transverse wave is represented by y = A sin(ωt − kx). For what value of the wavelength is the wave velocity equal to the maximum particle velocity?
(a) \( \frac{\pi A}{2} \)
(b) \( \pi A \)
(c) \( 2\pi A \)
(d) \( A \)
Show Answer & Explanation

Answer: (c) \( 2\pi A \)

Explanation:
1. Wave velocity = ω/k and maximum particle velocity = Aω.
2. Setting ω/k = Aω gives k = 1/A, so λ = 2π/k = 2πA.

Teacher's Note:
1. Equate ω/k with Aω.

Question 2:
Assertion (A): Solids can support both longitudinal and transverse waves but only longitudinal waves can propagate in gases.
Reason (R): For the propagation of transverse waves, the medium must also necessarily have the property of rigidity.
(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. Transverse waves need a shear (rigidity) modulus, which solids have and gases do not.
2. The reason explains the assertion.

Teacher's Note:
1. Rigidity needed for transverse waves.

Question 3: A closed organ pipe (closed at one end) is excited to support the third overtone. It is found that the air in the pipe has
(a) three nodes and three antinodes
(b) three nodes and four antinodes
(c) four nodes and three antinodes
(d) four nodes and four antinodes
Show Answer & Explanation

Answer: (d) four nodes and four antinodes

Explanation:
1. The third overtone is the 7th harmonic.
2. The closed end is a node and the open end an antinode, so there are 4 nodes and 4 antinodes.

Teacher's Note:
1. Count pairs: (2n − 1) harmonic has n nodes.

Question 4: The equation of the resultant wave obtained after superposition of two waves is y(x, t) = 2a sin kx cos ωt. The positions of the nodes are given by
(a) \( \sin kx=-1 \)
(b) \( \sin kx=0 \)
(c) \( \sin kx=1 \)
(d) \( \sin kx=\frac{n\pi}{2} \)
Show Answer & Explanation

Answer: (b) \( \sin kx=0 \)

Explanation:
1. Nodes have zero amplitude at all times.
2. That needs sin kx = 0.

Teacher's Note:
1. Amplitude is 2a sin kx.

Question 5: The Doppler effect is not applicable for
(a) audio waves
(b) electromagnetic waves
(c) shock waves
(d) none of these
Show Answer & Explanation

Answer: (d) none of these

Explanation:
1. The Doppler effect applies to all kinds of waves, including sound and light.

Teacher's Note:
1. It is general.

Question 6: A sonometer wire supports a 4 kg load and vibrates in the fundamental mode with a tuning fork of frequency 416 Hz. The length of the wire between the bridges is now doubled. In order to maintain the fundamental mode, the load should be changed to
(a) 1 kg
(b) 2 kg
(c) 4 kg
(d) 16 kg
Show Answer & Explanation

Answer: (d) 16 kg

Explanation:
1. f = (1/2L)√(T/μ), so for fixed f, T ∝ L².
2. Doubling L needs 4 times the tension, so the load is 16 kg.

Teacher's Note:
1. T ∝ L² at fixed f.

Question 7:
Assertion (A): The Doppler formula for sound waves is symmetric with respect to the speed of the source and the speed of the observer.
Reason (R): The motion of the source with respect to a stationary observer is not equivalent to the motion of an observer with respect to a stationary source.
(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 formula f′ = f(v ± v_o)/(v ∓ v_s) treats them differently, so the assertion is false.
2. The reason is true, because the medium is the reference for the speed of sound.

Teacher's Note:
1. The medium is the reference frame.

Question 8: Two vibrating tuning forks produce progressive waves given by Y₁ = 4 sin 500πt and Y₂ = 2 sin 506πt. The number of beats produced per minute is
(a) 360
(b) 180
(c) 60
(d) 3
Show Answer & Explanation

Answer: (b) 180

Explanation:
1. The frequencies are 250 Hz and 253 Hz.
2. There are 3 beats per second, or 180 per minute.

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

Question 9: The ratio of the speed of a body to the speed of sound is called
(a) Mach number
(b) Doppler ratio
(c) sonic index
(d) refractive index
Show Answer & Explanation

Answer: (a) Mach number

Explanation:
1. This ratio is the Mach number.

Teacher's Note:
1. Mach number = v/v_sound.

Question 10: The fundamental frequency of a closed organ pipe of length 20 cm is equal to the second overtone of an organ pipe open at both ends. The length of the open pipe is
(a) 100 cm
(b) 120 cm
(c) 140 cm
(d) 80 cm
Show Answer & Explanation

Answer: (b) 120 cm

Explanation:
1. Closed pipe: v/(4 × 0.2).
2. The second overtone of an open pipe is 3v/2L. Equating, L = 3 × 4 × 0.2/2 = 1.2 m = 120 cm.

Teacher's Note:
1. Match f₁ of closed with 3f₁ of open.

Question 11: The bulk modulus of a liquid of density 8000 kg/m³ is 2 × 10⁹ N/m². The speed of sound in that liquid is (in m/s)
(a) 200
(b) 250
(c) 100
(d) 500
Show Answer & Explanation

Answer: (d) 500

Explanation:
1. v = √(B/ρ) = √(2 × 10⁹/8000).
2. = √(2.5 × 10⁵) = 500 m/s.

Teacher's Note:
1. v = √(B/ρ).

Question 12: If wind blows from a stationary sounding object to a stationary listener, then the apparent frequency n′ and the actual frequency n are related as
(a) \( n'\ge n \)
(b) \( n' \lt n \)
(c) \( n'=n \)
(d) \( n' \gt n \)
Show Answer & Explanation

Answer: (c) \( n'=n \)

Explanation:
1. Wind changes the speed of sound relative to the ground, but the wavelength changes in the same proportion.
2. The number of waves reaching a stationary listener per second is unchanged, so n′ = n.

Teacher's Note:
1. Wind does not change the frequency.

Question 13:
Assertion (A): The fundamental frequency of an open organ pipe increases as the temperature is increased.
Reason (R): As the temperature increases, the velocity of sound increases more rapidly than the length of the pipe.
(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. f = v/2L, and v ∝ √T rises faster than the small thermal expansion of L.
2. So f increases.

Teacher's Note:
1. f = v/2L.

Question 14: The velocity of a moving galaxy is 300 km/s and the apparent change in wavelength of a spectral line emitted from one of the galaxy's stars is observed to be 0.5 nm. Then the actual wavelength of the spectral line is
(a) 3000 Å
(b) 5000 Å
(c) 6000 Å
(d) 4500 Å
Show Answer & Explanation

Answer: (b) 5000 Å

Explanation:
1. Δλ/λ = v/c = 3 × 10⁵/3 × 10⁸ = 10⁻³.
2. λ = 0.5 nm/10⁻³ = 500 nm = 5000 Å.

Teacher's Note:
1. Δλ/λ = v/c.

Question 15: Sound waves travel in a medium whose adiabatic elasticity is E and isothermal elasticity is E′. The velocity of sound waves is proportional to
(a) E
(b) \( \sqrt E \)
(c) \( \sqrt{E'} \)
(d) \( E/E' \)
Show Answer & Explanation

Answer: (b) \( \sqrt E \)

Explanation:
1. Laplace showed that sound propagates adiabatically.
2. So v = √(E/ρ) ∝ √E.

Teacher's Note:
1. Use the adiabatic modulus.

Question 16: For which of the following waves does the speed depend on temperature?
(a) light
(b) sound
(c) both (a) and (b)
(d) none of these
Show Answer & Explanation

Answer: (b) sound

Explanation:
1. The speed of sound in a gas is √(γRT/M), which depends on T.
2. The speed of light in vacuum does not.

Teacher's Note:
1. v ∝ √T for sound.

Question 17: The waves associated with the moving particles are called
(a) mechanical waves
(b) ultrasonic waves
(c) matter waves
(d) shock waves
Show Answer & Explanation

Answer: (c) matter waves

Explanation:
1. de Broglie associated a wave with every moving particle.
2. These are called matter waves.

Teacher's Note:
1. de Broglie waves.

Question 18: The pressure variations in the propagation of sound in a gaseous medium are
(a) adiabatic
(b) isothermal
(c) isobaric
(d) isochoric
Show Answer & Explanation

Answer: (a) adiabatic

Explanation:
1. Compressions and rarefactions are too rapid for heat exchange.
2. The variations are adiabatic.

Teacher's Note:
1. Laplace's correction.

Question 19: Two sources of sound placed close to each other emit progressive waves given by y₁ = 4 sin 600πt and y₂ = 5 sin 608πt. An observer located near these two sources of sound will hear
(a) 4 beats per second with intensity ratio 25 : 16 between waxing and waning
(b) 8 beats per second with intensity ratio 25 : 16 between waxing and waning
(c) 8 beats per second with intensity ratio 81 : 1 between waxing and waning
(d) 4 beats per second with intensity ratio 81 : 1 between waxing and waning
Show Answer & Explanation

Answer: (d) 4 beats per second with intensity ratio 81 : 1 between waxing and waning

Explanation:
1. The frequencies are 300 Hz and 304 Hz, so 4 beats per second.
2. I_max/I_min = (5 + 4)²/(5 − 4)² = 81 : 1.

Teacher's Note:
1. Amplitudes add and subtract.

Question 20: On reflection of a wave from a rarer medium, the change in phase is
(a) zero
(b) \( \pi/2 \)
(c) \( \pi \)
(d) \( 3\pi/4 \)
Show Answer & Explanation

Answer: (a) zero

Explanation:
1. At a free end or a rarer medium the wave is reflected without a phase change.

Teacher's Note:
1. Rarer medium: no phase change.

Question 21: For a sinusoidal wave y(x, t) = a sin(kx − ωt + φ) and a given a, the factor that determines the displacement of the wave at any position and at any instant is
(a) constant k
(b) angular velocity ω
(c) time interval t
(d) phase (kx − ωt + φ)
Show Answer & Explanation

Answer: (d) phase (kx − ωt + φ)

Explanation:
1. For a given amplitude, the displacement is a sin of the total phase.
2. The phase (kx − ωt + φ) fixes the displacement.

Teacher's Note:
1. y = a sin(phase).

Question 22: The number of possible natural oscillations of the air column in a pipe closed at one end, of length 85 cm, whose frequencies lie below 1250 Hz is (velocity of sound = 340 m/s)
(a) 4
(b) 5
(c) 7
(d) 6
Show Answer & Explanation

Answer: (d) 6

Explanation:
1. The frequencies are (2k + 1) × 340/(4 × 0.85) = (2k + 1) × 100 Hz.
2. Those below 1250 Hz are 100, 300, 500, 700, 900 and 1100 Hz, so there are 6.

Teacher's Note:
1. Closed pipe: odd multiples.

Question 23: If the intensities of two interfering waves are I₁ and I₂, the contrast between maximum and minimum intensity is maximum when
(a) \( I_1\gg I_2 \)
(b) \( I_1\ll I_2 \)
(c) \( I_1=I_2 \)
(d) \( \text{either }I_1\text{ or }I_2\text{ is zero} \)
Show Answer & Explanation

Answer: (c) \( I_1=I_2 \)

Explanation:
1. Contrast = (I_max − I_min)/(I_max + I_min) = 2√(I₁I₂)/(I₁ + I₂).
2. This is greatest (equal to 1) when I₁ = I₂.

Teacher's Note:
1. Equal intensities give perfect contrast.

Question 24: Which of the following statements is/are correct about waves? I. Waves are patterns of disturbance which move without the actual physical transfer of flow of matter as a whole. II. Waves cannot transport energy. III. The pattern of disturbance in the form of waves carries information that propagates from one point to another. IV. All our communications essentially depend on transmission of signals through waves.
(a) I and III
(b) only IV
(c) I, II and III
(d) I, III and IV
Show Answer & Explanation

Answer: (d) I, III and IV

Explanation:
1. Waves move a disturbance, not matter (I), carry information (III) and underlie communication (IV).
2. II is false because waves do transport energy.

Teacher's Note:
1. Waves carry energy and information.

Question 25: A tuning fork of frequency 512 Hz makes 4 beats per second with the vibrating string of a piano. The beat frequency decreases to 2 beats per second when the tension in the piano string is slightly increased. The frequency of the piano string before increasing the tension was
(a) 510 Hz
(b) 514 Hz
(c) 516 Hz
(d) 508 Hz
Show Answer & Explanation

Answer: (d) 508 Hz

Explanation:
1. Increasing the tension raises the string frequency.
2. The beats decrease, so the string frequency is approaching 512 Hz from below: it was 512 − 4 = 508 Hz.

Teacher's Note:
1. Tension up, frequency up.

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