Sound Waves for JEE Main: Complete Guide

Sound waves are longitudinal mechanical waves, and JEE Main tests them through speed-of-sound calculations, intensity and decibel problems, Doppler effect, resonance in pipes, and beats. The chapter is formula-dense but the problem types are highly predictable — learn the formulas with their conditions and you can systematically work through any sound-waves question the exam creates.

Speed of Sound

Speed of sound in an ideal gas: v = √(γRT/M), where γ = C_p/C_v, R = 8.314 J/(mol·K), T is temperature in Kelvin, and M is molar mass. For air at STP, v ≈ 331 m/s; at 20°C, v ≈ 343 m/s. Key proportionality: v ∝ √T, so doubling the absolute temperature increases speed by √2. Speed in liquids: v = √(B/ρ) where B is bulk modulus. Speed in solids: v = √(Y/ρ) where Y is Young's modulus. Sound travels fastest in solids and slowest in gases. For the wave properties context see our waves and oscillations guide.

Intensity, Loudness, and Decibels

Intensity I = Power/Area = P/(4πr²) for a point source (inverse-square law). Doubling the distance decreases intensity by four times. The decibel scale: β = 10 log₁₀(I/I₀) dB, where I₀ = 10⁻¹² W/m² (threshold of hearing). An increase of 10 dB means ten times the intensity; 3 dB ≈ double the intensity. If two sources each of loudness L₁ dB are superposed: the combined intensity is 2I₁, giving L_total = L₁ + 10 log₁₀(2) ≈ L₁ + 3 dB. This "+3 for double" shortcut solves many JEE intensity MCQs instantly.

Beats

When two sources of slightly different frequencies f₁ and f₂ superpose, the amplitude oscillates at the beat frequency |f₁ − f₂| beats per second. This is the number of times per second the sound intensifies. If a string vibrating at 264 Hz is heard with a tuning fork giving 4 beats per second, the fork's frequency is either 260 or 268 Hz. Tightening the string raises its frequency — if beats decrease, the string was below the fork (260 Hz); if beats increase, it was above (268 Hz). This reasoning pattern is a classic JEE question.

Doppler Effect

The observed frequency when source and observer move: f' = f × (v + v_o)/(v − v_s), where v is speed of sound, v_o is observer's speed (positive if moving toward source), v_s is source speed (positive if moving toward observer). The mnemonic: signs in the numerator and denominator are such that relative approach increases frequency, relative recession decreases it. Common exam trap: the formula changes if the medium is moving (wind). For the detailed treatment, see our Doppler effect guide.

Resonance in Pipes (Quick Review)

Open pipe: fundamental f₁ = v/(2L), all harmonics present. Closed pipe: fundamental f₁ = v/(4L), only odd harmonics. If a resonance column gives first resonance at 17 cm and second at 51 cm: λ/2 = 51 − 17 = 34 cm, so λ = 68 cm; v_sound = f × 68 cm. This standard experiment calculation is both a theory topic and a practical, worth memorising as a single unified procedure. After covering all sound-waves patterns, confirm mastery with a free mock test.