JEE Physics Waves MCQs Set 26

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Chapter-wise Objective Questions: Waves

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Multiple Choice Questions

Question 1: A pipe open at both ends will produce
(a) all the harmonics
(b) all the odd harmonics
(c) all the even harmonics
(d) none of the harmonics
Show Answer & Explanation

Answer: (a) all the harmonics

Explanation:
1. An open pipe has antinodes at both ends.
2. It supports frequencies f, 2f, 3f, …, that is all harmonics.

Teacher's Note:
1. Open pipe: all harmonics.

Question 2: The notes of frequencies which are integral multiples of the fundamental frequency are called
(a) beats
(b) harmonics
(c) antinodes
(d) tones
Show Answer & Explanation

Answer: (b) harmonics

Explanation:
1. Integral multiples of the fundamental frequency are harmonics.

Teacher's Note:
1. Harmonics are n × f₀.

Question 3:
Assertion (A): A sound wave is an example of a longitudinal wave.
Reason (R): In longitudinal waves, the constituents of the medium oscillate perpendicular to the direction of wave propagation.
(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: (c) A is true, but R is false.

Explanation:
1. Sound in a fluid consists of compressions and rarefactions along the direction of propagation.
2. The reason is false, since the particles oscillate parallel to the direction of propagation.

Teacher's Note:
1. Longitudinal means parallel.

Question 4: The equation y = a sin[(2π/λ)(vt − x)] is an expression for
(a) a stationary wave of single frequency along the x-axis
(b) a simple harmonic motion
(c) a progressive wave of single frequency along the x-axis
(d) the resultant of two SHMs of slightly different frequencies
Show Answer & Explanation

Answer: (c) a progressive wave of single frequency along the x-axis

Explanation:
1. The argument is a function of (vt − x), so it describes a wave moving along +x with one frequency.

Teacher's Note:
1. Function of (vt − x).

Question 5: A cylindrical tube, open at both ends, has a fundamental frequency f in air. The tube is dipped vertically in water so that half of it is in water. The fundamental frequency of the air column is now
(a) f
(b) \( \frac f2 \)
(c) \( \frac{3f}4 \)
(d) 2f
Show Answer & Explanation

Answer: (a) f

Explanation:
1. The air column is now a closed pipe of length L/2.
2. Its fundamental is v/(4 × L/2) = v/2L, which equals the original f.

Teacher's Note:
1. Closed pipe of half the length.

Question 6: What is the effect of humidity on sound waves when the humidity increases?
(a) speed of sound waves is more
(b) speed of sound waves is less
(c) speed of sound waves remains the same
(d) speed of sound waves becomes zero
Show Answer & Explanation

Answer: (a) speed of sound waves is more

Explanation:
1. Moist air is less dense than dry air at the same pressure.
2. The speed of sound is higher in humid air.

Teacher's Note:
1. Water vapour lowers the density.

Question 7:
Assertion (A): The base of the Laplace correction was that the exchange of heat between the region of compression and rarefaction in air is negligible.
Reason (R): Air is a bad conductor of heat and the velocity of sound in air is quite large.
(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. Air conducts heat poorly and the compressions pass quickly, so there is no time for heat exchange.
2. The reason explains the adiabatic assumption.

Teacher's Note:
1. Adiabatic propagation.

Question 8: A speeding motorcyclist sees a traffic jam ahead and slows down to 36 km/h. He finds that a car ahead of him moving at 18 km/h in the same direction is honking at a frequency of 1392 Hz. If the speed of sound is 343 m/s, the frequency of the honk as heard by him will be
(a) 1332 Hz
(b) 1372 Hz
(c) 1412 Hz
(d) 1464 Hz
Show Answer & Explanation

Answer: (c) 1412 Hz

Explanation:
1. The speeds are 10 m/s (observer) and 5 m/s (source), the source moving away in the direction of the observer's motion.
2. f′ = 1392 × (343 + 10)/(343 + 5) = 1412 Hz.

Teacher's Note:
1. f′ = f(v + v_o)/(v + v_s).

Question 9: Consider the three waves z₁ = A sin(kx − ωt), z₂ = A sin(kx + ωt) and z₃ = A sin(ky − ωt). Which of the following represents a standing wave?
(a) \( z_1+z_2 \)
(b) \( z_2+z_3 \)
(c) \( z_3+z_1 \)
(d) \( z_1+z_2+z_3 \)
Show Answer & Explanation

Answer: (a) \( z_1+z_2 \)

Explanation:
1. z₁ + z₂ = 2A sin kx cos ωt.
2. This is a standing wave, from two equal waves travelling in opposite directions along x.

Teacher's Note:
1. Opposite directions, same axis.

Question 10: The velocity of sound in a gas
(a) increases by about 0.61 m/s when the temperature rises by 1°C
(b) decreases by 0.61 m/s when the temperature rises by 1°C
(c) depends upon the pressure of the gas at constant temperature
(d) depends upon the coefficient of shearing of the gas
Show Answer & Explanation

Answer: (a) increases by about 0.61 m/s when the temperature rises by 1°C

Explanation:
1. v ≈ 331 + 0.61 t (in m/s, t in °C).
2. So it increases by about 0.61 m/s per °C.

Teacher's Note:
1. Temperature coefficient of sound speed.

Question 11: Which of the following represents the equation of a spherical progressive wave?
(a) \( y=a\sin\omega t \)
(b) \( y=a\sin(\omega t-kr) \)
(c) \( y=\frac{a}{\sqrt2}\sin(\omega t-kr) \)
(d) \( y=\frac ar\sin(\omega t-kr) \)
Show Answer & Explanation

Answer: (d) \( y=\frac ar\sin(\omega t-kr) \)

Explanation:
1. In a spherical wave the intensity falls as 1/r², so the amplitude falls as 1/r.
2. So y = (a/r) sin(ωt − kr).

Teacher's Note:
1. Amplitude ∝ 1/r.

Question 12: The speed of sound is maximum in
(a) solids
(b) liquids
(c) gases
(d) depends on the temperature of the medium
Show Answer & Explanation

Answer: (a) solids

Explanation:
1. Solids have much higher elastic moduli than liquids and gases for comparable density.
2. So the speed of sound is greatest in solids.

Teacher's Note:
1. Stiffer medium, faster sound.

Question 13:
Assertion (A): To hear distinct beats, the difference in frequencies of two sources should not be greater than 10.
Reason (R): The persistence of the human ear is 1/10 second.
(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. The ear cannot separate sound variations that are less than 0.1 s apart.
2. So only up to about 10 beats per second are distinct.

Teacher's Note:
1. Persistence of hearing 0.1 s.

Question 14: When two sound waves are superimposed, beats are produced when they have different
(a) amplitudes and phases
(b) velocities
(c) phases
(d) frequencies
Show Answer & Explanation

Answer: (d) frequencies

Explanation:
1. Beats need two waves of slightly different frequency.

Teacher's Note:
1. Beats come from a frequency difference.

Question 15: A train moving at a speed of 220 m/s towards a stationary object emits a sound of frequency 1000 Hz. Some of the sound reaching the object gets reflected back to the train as an echo. The frequency of the echo as detected by the driver of the train is (speed of sound in air = 330 m/s)
(a) 3500 Hz
(b) 4000 Hz
(c) 5000 Hz
(d) 3000 Hz
Show Answer & Explanation

Answer: (c) 5000 Hz

Explanation:
1. The object receives f₁ = 1000 × 330/(330 − 220) = 3000 Hz.
2. It reflects this frequency, and the driver detects 3000 × (330 + 220)/330 = 5000 Hz.

Teacher's Note:
1. Apply Doppler twice.

Question 16: Which of the following statements is/are correct about the standing wave? I. In a standing wave the disturbance produced is confined to the region where it is produced. II. In a standing wave, all the particles cross their mean position together. III. In a standing wave, energy is transmitted from one region of space to another.
(a) I and II
(b) only II
(c) I and III
(d) I, II and III
Show Answer & Explanation

Answer: (a) I and II

Explanation:
1. A standing wave does not travel, and all particles reach the mean position at the same instants.
2. There is no transmission of energy, so III is false.

Teacher's Note:
1. No energy flow in a standing wave.

Question 17: Match Column I with Column II.
Column IColumn II
(A) Sound(1) Frequency
(B) SONAR(2) Mechanical wave
(C) Reflection of sound(3) Finding depth of the sea
(D) Pitch(4) Echo

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

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

Explanation:
1. Sound is a mechanical wave (A-2).
2. SONAR is used to find the depth of the sea (B-3).
3. Reflection of sound gives an echo (C-4).
4. Pitch depends on frequency (D-1).

Teacher's Note:
1. Simple definitions.

Question 18: An organ pipe P₁ closed at one end vibrating in its first overtone and another pipe P₂ open at both ends vibrating in the third overtone are in resonance with a given tuning fork. The ratio of the length of P₁ to that of P₂ is
(a) \( 8/3 \)
(b) \( 3/8 \)
(c) \( 1/2 \)
(d) \( 1/3 \)
Show Answer & Explanation

Answer: (b) \( 3/8 \)

Explanation:
1. P₁: 3v/4L₁; P₂ (4th harmonic): 4v/2L₂ = 2v/L₂.
2. Equating gives L₁/L₂ = 3/8.

Teacher's Note:
1. Match the frequencies.

Question 19: Waves produced by a motor boat sailing in water are
(a) only longitudinal
(b) only transverse
(c) both longitudinal and transverse
(d) neither longitudinal nor transverse
Show Answer & Explanation

Answer: (c) both longitudinal and transverse

Explanation:
1. Water-surface waves involve both up-and-down and to-and-fro motion of the water particles.
2. So they are a combination of transverse and longitudinal waves.

Teacher's Note:
1. Surface waves are mixed.

Question 20: Match Column I with Column II.
Column IColumn II
(A) Mechanical waves(1) Disturbance for a short time
(B) Pulse(2) Independent of the amplitude of vibrations
(C) Velocity of sound in air(3) SONAR
(D) Tracking of fish in the ocean(4) Require a material medium

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

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

Explanation:
1. Mechanical waves need a material medium (A-4).
2. A pulse is a disturbance for a short time (B-1).
3. The speed of sound does not depend on amplitude (C-2).
4. Fish are tracked using SONAR (D-3).

Teacher's Note:
1. Link each term to its property.

Question 21: The speed of a mechanical wave is determined by
(a) inertial properties of the medium
(b) elastic properties of the medium
(c) both (a) and (b)
(d) none of these
Show Answer & Explanation

Answer: (c) both (a) and (b)

Explanation:
1. v = √(elasticity/inertia), for example √(E/ρ) or √(T/μ).
2. Both properties of the medium matter.

Teacher's Note:
1. v = √(elastic/inertial).

Question 22: The SI unit of the propagation constant k is
(a) rad m⁻¹
(b) m rad⁻¹
(c) rad m
(d) unitless
Show Answer & Explanation

Answer: (a) rad m⁻¹

Explanation:
1. k = 2π/λ is the phase change per unit length.
2. Its unit is rad/m.

Teacher's Note:
1. k = 2π/λ.

Question 23:
Assertion (A): Compression and rarefaction involve changes in density and pressure.
Reason (R): When particles are compressed, the density of the medium increases and when they are rarefied, the density of the medium decreases.
(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. In a compression the same mass occupies less volume, raising density and pressure.
2. The reason explains the changes mentioned in the assertion.

Teacher's Note:
1. Compression: higher density and pressure.

Question 24: Two waves are represented by y₁ = a sin(ωt + kx + 0.57) m and y₂ = a cos(ωt + kx) m, where x is in metres and t in seconds. The phase difference between them is
(a) 1.0 radian
(b) 1.25 radian
(c) 1.57 radian
(d) 0.57 radian
Show Answer & Explanation

Answer: (a) 1.0 radian

Explanation:
1. y₂ = a sin(ωt + kx + π/2).
2. The phase difference is π/2 − 0.57 = 1.57 − 0.57 = 1.0 rad.

Teacher's Note:
1. Convert cos to sin.

Question 25: Which of the following statements related to organ pipes is/are correct? I. In a closed organ pipe, longitudinal standing waves are present. II. In a closed organ pipe only odd harmonics are present. III. The harmonics present in a pipe open at both ends are odd harmonics only.
(a) only I
(b) II and III
(c) I and II
(d) I, II and III
Show Answer & Explanation

Answer: (c) I and II

Explanation:
1. A closed pipe has standing longitudinal waves with only odd harmonics.
2. An open pipe has all harmonics, so III is false.

Teacher's Note:
1. Closed: odd.
2. Open: all.

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