Sound Waves – Properties, Behavior & Applications Explained | Chapter 16 of University Physics

Chapter 16 explores how sound waves propagate through different media and manifest in phenomena like resonance, interference, beats, and the Doppler effect. You’ll learn the basics of longitudinal mechanical waves, how we measure and perceive them, and their critical applications in acoustics and engineering.

Watch the full video summary here for detailed explanations and demonstrations.

What Is a Sound Wave?

• Longitudinal wave: particles oscillate parallel to wave propagation.
• Audible range: 20 Hz to 20 kHz (infrasonic below, ultrasonic above).
• Phase relation: pressure and displacement are 90° out of phase.
• Pressure wave model: p(x, t) = B k A sin(kx – ωt).

Speed of Sound

• In fluids: v = √(B/ρ), where B is bulk modulus.
• In solids: v = √(Y/ρ), with Y Young’s modulus.
• In gases: v = √(γRT/M), rising with temperature.
• Wavelength relation: λ = v/f.

Sound Intensity & Decibels

Intensity (I) measures power per area: I = ½ ρ v ω² A². The decibel scale expresses sound level:

β = 10 log₁₀(I/I₀), where I₀ = 10⁻¹² W/m². Intensity follows an inverse-square law: I ∝ 1/r²; a +10 dB increase is a tenfold intensity rise.

Standing Waves in Pipes

Boundary conditions create resonant modes:

• Open pipe (both ends): pressure nodes at ends, fₙ = n v/(2L).
• Closed pipe (one end): pressure antinode at closed end, fₙ = n v/(4L) for n = 1,3,5….

Timbre and harmonic content depend on pipe geometry and boundary conditions.

Resonance & Beats

• Resonance: large oscillations when driving frequency matches a natural frequency.
• Beats: interference of two close frequencies producing beat frequency f_beat = |f₁ – f₂|.

Doppler Effect & Shock Waves

The observed frequency shifts when source or listener moves:

f_obs = f_src (v + v_listener)/(v + v_source). Supersonic sources generate shock waves and sonic booms; the Mach number M = v_source/v determines the Mach angle by sin θ = 1/M.

Conclusion

Sound waves are fundamental to acoustics, communication, and diagnostics. By mastering wave parameters, intensity scales, standing wave modes, resonance, beats, and Doppler shifts, you’ll understand both everyday phenomena and specialized engineering applications such as sonar, audio design, and medical ultrasound.

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