Waves & Sound — Part 1: 40 MCQs with Explanations

Gamma rays have the highest frequency (and shortest wavelength) in the electromagnetic spectrum.

At resonance, X_L = X_C, so they cancel each other. Impedance Z = √[R² + (X_L - X_C)²] = R (minimum value).

When source approaches observer, waves get compressed, wavelength decreases, frequency increases.

Diffraction is the bending of waves around obstacles or through openings.

In SHM, x = A sin(ωt). For x = A/2: A/2 = A sin(ωt) ⇒ sin(ωt) = 1/2 ⇒ ωt = π/6 ⇒ t = T/12.

φ = hν₀ ⇒ ν₀ = φ/h = (2.3 × 1.6 × 10^-19)/(6.63 × 10^-34) ≈ 5.55 × 10^14 Hz.

Natural frequency f = 1/(2π√(LC)).

Q = ω₀L/R = 1/(ω₀CR) = (1/R)√(L/C) for series RLC circuit at resonance.

Stopping potential V₀ = (h/e)ν - φ/e depends on frequency ν and work function φ, not on intensity.

At resonance, circuit is purely resistive (X_L = X_C), so power factor = cos0° = 1.

Since v = c/n and frequency remains constant, λₘ = v/f = (c/n)/f = λ₀/n, where λ₀ is wavelength in vacuum.

Planck's quantum theory: E = hf, where h is Planck's constant (6.63 × 10⁻³⁴ J·s).

Work function φ = hf₀, where f₀ is threshold frequency. f₀ = φ/h = 2.3/(4.14 × 10⁻¹⁵) = 5.56 × 10¹⁴ Hz.

Q-factor = ω₀L/R = 1/ω₀CR for series resonance, where ω₀ = 1/√(LC) is resonant frequency.

Frequency f = 1/T = (1/2π)√(g/l), where T = 2π√(l/g) is time period.

Capacitive reactance Xc = 1/ωC, where ω = 2πf is angular frequency.

At resonance, inductive reactance equals capacitive reactance: ωL = 1/ωC, so ω = 1/√(LC).

Photoelectric effect is emission of electrons (photoelectrons) from material upon electromagnetic radiation exposure above threshold frequency.

Standard frequency for AC power supply in Pakistan and most of Europe/Asia is 50 Hz. North America uses 60 Hz.

Gamma rays have the shortest wavelength (and highest frequency) in the electromagnetic spectrum, typically < 10^-11 m.

Polarization is restriction of electric field vector to vibrate in a single plane perpendicular to direction of propagation.

E = hν, so energy directly proportional to frequency ν. Since c = νλ, E = hc/λ, so inversely proportional to wavelength.

Photoelectric effect (threshold frequency, instantaneous emission, K_max ∝ ν) can only be explained by particle (quantum) nature of light.

de Broglie proposed that particles exhibit wave properties (λ = h/p) and waves exhibit particle properties (photons).

Threshold frequency ν₀ = φ/h depends only on work function φ of metal surface, not on light intensity.

Gamma rays are electromagnetic radiation (photons) of very high frequency emitted by excited nucleus.

At resonance frequency f₀ = 1/(2π√(LC)), X_L = X_C, impedance minimum (Z = R), current maximum, power factor = 1.

Q = ω₀L/R = 1/(ω₀CR) = resonant frequency/bandwidth. High Q means sharp resonance peak.

Form factor = V_rms/V_avg (for half-cycle). For sine wave: V_rms = V₀/√2, V_avg = 2V₀/π, so form factor = π/(2√2) ≈ 1.11.

Peak factor = V₀/V_rms = √2 ≈ 1.414 for sine wave.

EM waves are transverse: electric and magnetic field vectors oscillate perpendicular to direction of propagation and to each other.

c = 1/√(μ₀ε₀) ≈ 3 × 10^8 m/s = 3 × 10^10 cm/s.

Radio waves have longest wavelength (≥ 1 mm) and lowest frequency in EM spectrum.

Microwaves (wavelength ~1 mm to 30 cm) are used in radar due to their ability to penetrate atmosphere and reflect from objects.

Threshold frequency ν₀ = φ/h, where φ = work function of metal.

Mechanical waves require a medium to travel because they propagate through the vibration of material particles. Examples include sound waves, water waves, and waves on a string.

The speed of sound in air at 0°C is 332 m/s. It increases with an increase in temperature. 340 m/s is the approximate speed at room temperature (around 20°C).

Destructive interference occurs when the crest of one wave meets the trough of another wave (phase difference of 180° or π radians). If they have the same amplitude, they cancel each other out completely.

Beats are the periodic variation in amplitude at a point due to the superposition of two waves having slightly different frequencies. The beat frequency is the difference between the two frequencies.

Nodes are points in a standing wave that remain stationary (zero amplitude). They occur at points where destructive interference consistently happens. Antinodes are points of maximum amplitude.