Waves Basics — Set 2

Correct Answer: C. Diffraction

• **Diffraction** = the spreading of waves around the edges of an obstacle or through a small opening, into the geometric shadow region. • **Most pronounced** when obstacle/aperture size ≈ wavelength; sound (λ ≈ 0.03–17 m) diffracts more easily around door edges than light (λ ≈ 400–700 nm). • 💡 Wrong-option analysis: Reflection: bouncing back from a surface — does not involve spreading into shadow; Refraction: change in direction when entering a new medium — caused by speed change, not obstacle edges; Polarization: orientation of transverse wave vibration — not bending around obstacles.

Correct Answer: C. Sum of displacements

• **Sum of displacements** = the superposition principle states that when two or more waves overlap, the total displacement at any point equals the algebraic (vector) sum of the individual displacements. • **After overlap**: waves pass through each other unchanged — the principle applies to linear (small-amplitude) waves. • 💡 Wrong-option analysis: Difference of frequencies only: beat frequency = |f₁ − f₂| — a result of superposition, not the principle itself; Always zero: only if waves are of equal amplitude and opposite phase at every point simultaneously; Product of displacements: no physical basis — displacements add, not multiply.

Correct Answer: D. Nodes

• **Nodes** = points in a standing wave where destructive interference is permanent — the two constituent waves always cancel at nodes, so the medium never moves there. • **Node spacing = λ/2**; adjacent nodes are separated by half a wavelength; antinodes (maximum displacement) lie midway between nodes. • 💡 Wrong-option analysis: Troughs: lowest points of a transverse wave at an instant — not a standing-wave fixed point; Antinodes: points of maximum displacement — the opposite of nodes; Crests: highest points of a transverse wave at an instant — not a fixed zero-displacement point.

Correct Answer: D. |f1 − f2|

• **|f₁ − f₂|** = beats arise from the superposition of two frequencies; the combined amplitude rises and falls at the rate equal to the absolute frequency difference. • **Practical range**: beats are heard distinctly when |f₁ − f₂| ≤ ~15 Hz; used to tune instruments by zeroing the beat rate. • 💡 Wrong-option analysis: f₁ × f₂: product of frequencies — appears in non-linear mixing, not simple beats; f₁ + f₂: sum frequency — not the beat frequency; f₁ / f₂: ratio — used for musical interval identification, not beats.

Correct Answer: C. Frequency due to relative motion

• **Frequency due to relative motion** = when source and observer move relative to each other, the spacing of wavefronts received by the observer changes, altering the observed frequency. • **Doppler formula**: f_obs = f × (v + v_obs)/(v − v_s) — approaching source raises observed pitch; receding lowers it. • 💡 Wrong-option analysis: Wavelength due to reflection only: reflection changes direction but not wavelength for a stationary reflector; Speed of wave due to source mass: wave speed depends on the medium, not the source's mass; Amplitude due to distance: intensity (∝ amplitude²) decreases with distance — this is not the Doppler effect.

Correct Answer: D. Transverse waves

• **Transverse waves** = polarization is the restriction of the transverse vibration direction to a single plane; only transverse waves have a vibration direction perpendicular to propagation that can be filtered. • **Example**: polaroid sunglasses filter light (transverse EM wave); sound (longitudinal) cannot be polarized because particles vibrate only along the propagation direction. • 💡 Wrong-option analysis: All waves equally: longitudinal waves cannot be polarized — this is wrong; Only sound waves: sound is longitudinal in air — cannot be polarized; Only longitudinal waves: polarization is exclusively for transverse waves.

Correct Answer: D. 3 × 10^8 m/s

• **3 × 10⁸ m/s** = the speed of light in vacuum (c), a fundamental physical constant used in all electromagnetic wave calculations. • **c = 299,792,458 m/s** ≈ 3 × 10⁸ m/s; in glass (n ≈ 1.5), light slows to ~2 × 10⁸ m/s. • 💡 Wrong-option analysis: 3 × 10⁷ m/s: 10× too slow — this would imply a refractive index of ~10 in vacuum, impossible; 3 × 10⁵ m/s: 1000× too slow — close to sound speed in solids, not light; 3 × 10⁶ m/s: 100× too slow — not the vacuum speed of light.

Correct Answer: A. Parallel to the direction of propagation

• **Parallel to the direction of propagation** = in a longitudinal wave, compressions and rarefactions form along the travel direction, so particles oscillate back and forth along that same direction. • **Example**: sound in air — air molecules move along the direction the sound wave travels; this is why sound cannot be polarized. • 💡 Wrong-option analysis: Perpendicular to the direction of propagation: this describes a transverse wave (light, string waves); In circles only: circular motion occurs in some surface waves (deep water waves) — not a general feature of longitudinal waves; Not at all: if particles did not move, there would be no wave.

Correct Answer: B. Phase

• **Phase** = a wavefront is a surface connecting all points that are in the same phase of oscillation — they reach their maximum (or any given) displacement simultaneously. • **For a point source**: wavefronts are concentric spheres (3D) or circles (2D); for a distant source: planar wavefronts. • 💡 Wrong-option analysis: Amplitude: amplitude can vary across a wavefront (e.g., decreasing with distance) — not the defining property; Speed: all points in a uniform medium travel at the same speed, but speed is not what a wavefront defines; Frequency: frequency is the same everywhere in a uniform medium — not what a wavefront connects.

Correct Answer: D. Interference

• **Interference** = light reflects from the outer and inner surfaces of the thin soap film; the two reflected beams overlap and interfere — constructive for certain wavelengths (colours) and destructive for others. • **Thin film condition**: 2nt = (m + ½)λ for bright fringe in reflection (t = film thickness, n = refractive index). • 💡 Wrong-option analysis: Doppler effect: requires relative motion between source and observer — not present in a stationary soap bubble; Refraction only: refraction changes direction at the film boundaries — does not produce colour patterns; Diffraction only: spreading around edges — not the mechanism for thin-film colours.