In beta decay, a neutron converts to a proton. Which particle is emitted?

The correct answer is B: Beta particle (electron) and antineutrino. In β⁻ decay, a neutron converts to proton, emitting electron and antineutrino: n → p + e⁻ + ν̄ₑ

A gas sample undergoes a process where pressure decreases linearly with volume: P = P₀ - kV, where k is a constant. For 1 mole of ideal gas at constant temperature, what is the work done when volume changes from V₁ to V₂?

The correct answer is A: P₀(V₂ - V₁) - k(V₂² - V₁²)/2. Work done: W = ∫P dV = ∫(P₀ - kV) dV from V₁ to V₂ = [P₀V - kV²/2] from V₁ to V₂ = P₀(V₂ - V₁) - k(V₂² - V₁²)/2

The intensity at a point in the interference pattern of two coherent sources is I₁ and I₂. The resultant intensity is maximum when the phase difference is:

The correct answer is B: 0 or 2π. Maximum intensity occurs for constructive interference when phase difference = 0 or 2π. I_max = (√I₁ + √I₂)²

A transverse wave on a string has amplitude A, wavelength λ, and speed v. The maximum velocity of a particle is:

The correct answer is B: 2πAv/λ. Maximum particle velocity = ωA = 2πfA = 2πA(v/λ) = 2πAv/λ

A standing wave on a string has nodes at x = 0 and x = 2 m. The wavelength is:

The correct answer is C: 4 m. Distance between two consecutive nodes = λ/2. If nodes are at 0 and 2 m, then λ/2 = 2, so λ = 4 m

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Waves

Physics questions for JEE Main — Mechanics, Electrostatics, Optics, Modern Physics.

100 Q 9 Topics Take Mock Test

Difficulty: All Easy Medium Hard 1–10 of 100

Topics in JEE Physics

All Mechanics 100 Thermodynamics 100 Electrostatics 100 Current Electricity 100 Magnetism 100 Optics 100 Modern Physics 100 Semiconductors 100 Waves 100

Q.1 Medium Waves

A tuning fork of frequency 512 Hz is held above the open end of a resonance tube containing water. The tube is gradually filled with water and resonance is first observed when the water level is 16.2 cm below the open end. Taking speed of sound as 340 m/s, what is the effective length of the air column at first resonance and why?

A 15 cm; because odd multiple of λ/4 is required for open pipe resonance

B 16.2 cm; because even multiple of λ/4 is required for closed pipe resonance

C 17.2 cm; due to end correction of approximately 1 cm for the open end

D 14.2 cm; due to end correction of approximately 2 cm for the open end

Correct Answer: C. 17.2 cm; due to end correction of approximately 1 cm for the open end

EXPLANATION

For a tube closed at one end (water surface), first resonance occurs at L = λ/4. Given f = 512 Hz, v = 340 m/s, λ = v/f = 340/512 ≈ 0.664 m. So λ/4 ≈ 0.166 m = 16.6 cm. The effective length includes end correction (≈1 cm for open end), so L_eff = 16.2 + 1 = 17.2 cm, which equals λ/4 within measurement precision.

Test

Q.2 Easy Waves

A transverse wave travels along a stretched string with equation y = 0.02sin(50πt - 4πx), where x and y are in meters and t is in seconds. What is the wave velocity and wavelength of this wave?

A v = 12.5 m/s, λ = 0.5 m

B v = 6.25 m/s, λ = 1 m

C v = 25 m/s, λ = 0.25 m

D v = 12.5 m/s, λ = 1 m

Correct Answer: A. v = 12.5 m/s, λ = 0.5 m

EXPLANATION

From y = 0.02sin(50πt - 4πx), comparing with y = Asin(ωt - kx): ω = 50π rad/s, k = 4π rad/m. Wavelength λ = 2π/k = 2π/(4π) = 0.5 m. Wave velocity v = ω/k = 50π/(4π) = 12.5 m/s.

Test

Q.3 Easy Waves

A wave traveling in the positive x-direction reflects from a fixed end. What is the phase change upon reflection?

A 0°

B 90°

C 180°

D 270°

Correct Answer: C. 180°

EXPLANATION

When a wave reflects from a fixed (denser) end, it undergoes a phase change of π radians or 180°

Test

Q.4 Hard Waves

A wave undergoes constructive interference with another identical wave. The resulting amplitude is A₀. If one wave's amplitude is reduced to half, what is the new resultant amplitude for constructive interference?

A A₀/4

B 3A₀/4

C A₀/2

D 3A₀/2

Correct Answer: D. 3A₀/2

EXPLANATION

Original: A₀ = A + A = 2A, so A = A₀/2. New amplitude = A₀/2 + A₀/4 = 3A₀/4 (if each gets halved) or A + A/2 = 3A/2 = 3A₀/4. Actually, new = A₀/2 + A₀/2 = A₀ or (A₀/2)/2 + A₀/2 = 3A₀/4

Test

Q.5 Medium Waves

A source emits sound with intensity 10⁻⁸ W/m² at a distance of 1 m. Assuming spherical spreading, what is the intensity at 10 m distance?

A 10⁻¹⁰ W/m²

B 10⁻⁹ W/m²

C 10⁻⁸ W/m²

D 10⁻⁷ W/m²

Correct Answer: A. 10⁻¹⁰ W/m²

EXPLANATION

Intensity ∝ 1/r². I₂/I₁ = (r₁/r₂)² = (1/10)² = 1/100. I₂ = 10⁻⁸/100 = 10⁻¹⁰ W/m²

Test

Q.6 Medium Waves

A progressive wave has amplitude 5 cm and wavelength 20 cm. Two points on the wave separated by 10 cm have a phase difference of:

A π/2

B π

C 2π

D π/4

Correct Answer: A. π/2

EXPLANATION

Phase difference = (2π/λ) × path difference = (2π/20) × 10 = π radian

Test

Q.7 Medium Waves

An organ pipe closed at one end has fundamental frequency 200 Hz. What is the frequency of the next possible resonance?

A 300 Hz

B 400 Hz

C 500 Hz

D 600 Hz

Correct Answer: D. 600 Hz

EXPLANATION

A closed organ pipe resonates at odd multiples: f₁, 3f₁, 5f₁... The next resonance after 200 Hz is 3×200 = 600 Hz

Test

Q.8 Medium Waves

A standing wave is formed on a string with equation y = 2cos(πx)sin(100πt) cm. What is the wavelength?

A 1 cm

B 2 cm

C π cm

D 100 cm

Correct Answer: B. 2 cm

EXPLANATION

From y = A cos(kx) sin(ωt), we have k = π, so λ = 2π/k = 2π/π = 2 cm

Test

Q.9 Medium Waves

A light wave travels from a denser medium (refractive index 1.5) to a rarer medium (refractive index 1.0). If the angle of incidence is 30°, what is the angle of refraction?

A 19.47°

B 30°

C 45°

D 48.75°

Correct Answer: D. 48.75°

EXPLANATION

Using Snell's law: n₁sin(θ₁) = n₂sin(θ₂). 1.5 × sin(30°) = 1 × sin(θ₂). θ₂ = 48.75°

Test

Q.10 Easy Waves

Two sources produce sound waves of frequencies 250 Hz and 254 Hz. What is the beat frequency heard?

A 2 Hz

B 4 Hz

C 6 Hz

D 254 Hz

Correct Answer: B. 4 Hz

EXPLANATION

Beat frequency = |f₁ - f₂| = |250 - 254| = 4 Hz

Test

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