Waves Basics — Set 1

Correct Answer: C. Frequency

• **Frequency** = frequency is set by the vibrating source and does not change at a boundary; speed and wavelength both adjust in the new medium. • **v = fλ**: when v changes and f stays fixed, λ = v/f changes proportionally — this is why colours (frequencies) of light don't change at a glass surface. • 💡 Wrong-option analysis: Wave speed: changes because the elastic/optical properties of the new medium differ; Amplitude: can decrease due to reflection losses — not guaranteed to stay constant; Wavelength: changes whenever speed changes (λ = v/f with f fixed).

Correct Answer: D. Transverse wave

• **Transverse wave** = particles of the medium vibrate perpendicular (at right angles) to the direction of wave propagation. • **Examples**: light waves, waves on a stretched string, ripples on a water surface — all transverse; sound in air is NOT transverse. • 💡 Wrong-option analysis: Longitudinal wave: particles vibrate parallel to propagation — compressions and rarefactions; Stationary wave: a pattern formed by two counter-propagating waves — not a wave type by particle motion; Progressive wave: a wave that travels forward — describes motion, not the vibration direction.

Correct Answer: C. Time period

• **Time period (T)** = the time for one complete oscillation; its SI unit is the second (s). • **T = 1/f**: if f = 50 Hz, T = 0.02 s — doubling frequency halves the period. • 💡 Wrong-option analysis: Frequency: number of cycles per second — not the time for one cycle; Amplitude: maximum displacement from equilibrium — not a time quantity; Wavelength: spatial length of one cycle — a distance, not a time.

Correct Answer: D. Wavelength

• **Wavelength (λ)** = the spatial distance over which one complete wave cycle repeats; in a longitudinal wave, it is the distance from one compression to the next (or rarefaction to rarefaction). • **v = fλ**: at 343 m/s and 343 Hz, λ = 1 m — a useful benchmark for sound in air. • 💡 Wrong-option analysis: Amplitude: maximum particle displacement — a distance but perpendicular to propagation; Wave speed: how fast the pattern advances — m/s, not a length; Time period: time for one cycle — not a spatial distance.

Correct Answer: C. Longitudinal mechanical waves

• **Longitudinal mechanical waves** = in air, sound particles vibrate parallel to the direction of propagation (compressions and rarefactions), requiring a material medium. • **Mechanical wave**: needs a medium — sound cannot travel in vacuum; it is not electromagnetic. • 💡 Wrong-option analysis: Electromagnetic waves: self-propagating electric/magnetic fields — no medium needed; Transverse waves: particles vibrate perpendicular to propagation — water waves yes, sound in air no; Waves that do not need a medium: electromagnetic waves (light) fit this — sound does not.

Correct Answer: C. Light wave

• **Light wave** = light is an electromagnetic transverse wave that requires no material medium — it propagates via oscillating electric and magnetic fields. • **c = 3 × 10⁸ m/s** in vacuum; electromagnetic waves span radio to gamma rays, all needing no medium. • 💡 Wrong-option analysis: Sound wave: mechanical longitudinal wave — needs air or another medium; Seismic wave: P-waves (longitudinal) and S-waves (transverse) — both mechanical, needing the Earth; Water wave: mechanical surface wave — needs the water medium.

Correct Answer: A. v = fλ

• **v = fλ** = wave speed equals frequency times wavelength; each cycle, the wave advances exactly one wavelength, and cycles per second times metres per cycle gives metres per second. • **Example**: sound at 440 Hz with λ = 0.78 m → v = 343 m/s; light at 6×10¹⁴ Hz with λ = 500 nm → v = 3×10⁸ m/s. • 💡 Wrong-option analysis: v = f + λ: dimensionally inconsistent — m/s ≠ Hz + m; v = f/λ: gives Hz/m, not m/s; v = λ/f: gives m/Hz = m·s — wrong units.

Correct Answer: D. Half

• **Half** = from v = fλ, if v is constant and f doubles, then λ = v/f is halved. • **Inverse relationship**: at constant speed, frequency and wavelength are inversely proportional — doubling one halves the other. • 💡 Wrong-option analysis: Unchanged: only true if speed also doubles; Four times: would require frequency to be halved, not doubled; Double: doubling both f and λ would double v, contradicting constant v.

Correct Answer: D. Frequency

• **Frequency** = pitch is the subjective perception corresponding to frequency; higher frequency → higher pitch, lower frequency → lower pitch. • **A4 = 440 Hz** produces a higher pitch than A3 = 220 Hz — one octave difference = factor of 2 in frequency. • 💡 Wrong-option analysis: Amplitude: controls loudness, not pitch; Distance from source: affects intensity — not pitch; Speed of sound: a medium property — does not directly change pitch.

Correct Answer: D. Intensity (linked to amplitude)

• **Intensity (linked to amplitude)** = loudness is the subjective sensation; the objective physical quantity is intensity (W/m²), which is proportional to amplitude². • **I ∝ A²**: doubling amplitude quadruples intensity, noticeably increasing perceived loudness. • 💡 Wrong-option analysis: Wavelength: related to pitch (via frequency) — not to loudness; Frequency only: determines pitch — loudness is primarily from amplitude/intensity; Time period only: inverse of frequency — a pitch-related quantity.