Download JEE MCQs for JEE Physics: Waves
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Chapter-wise Objective Questions: Waves
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Multiple Choice Questions
(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.
(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.
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.
(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).
(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.
(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.
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.
(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).
(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.
(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.
(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.
(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.
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.
(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.
(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.
(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.
| Column I | Column 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.
(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.
(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.
| Column I | Column 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.
(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).
(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.
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.
(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.
(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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FAQs
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