Describe the longitudinal nature of sound waves

3.4 Sound – Longitudinal Nature of Sound Waves

3.4.1 Production of Sound by a Vibrating Source

• A sound‑producing source (e.g. a tuning‑fork, a loud‑speaker diaphragm, a plucked string) vibrates back‑and‑forth about its equilibrium position.
• The vibration creates alternating regions of high and low pressure in the surrounding medium.

  • Greater vibration amplitude → larger pressure variation → louder sound.

3.4.2 Audible Frequency Range

Human ears can detect frequencies from 20 Hz to 20 kHz. Within this range:

• Pitch increases with frequency.
• Loudness is related to the amplitude of the pressure variation (≈ 20 dB – 120 dB SPL for typical sounds).

3.4.3 Why a Material Medium Is Required

Sound is a mechanical wave; it needs a material that can be compressed and rarefied. In a vacuum there are no particles to oscillate, so sound cannot travel.

3.4.4 What Is a Longitudinal Wave?

A longitudinal wave is a disturbance in which the particles of the medium vibrate parallel to the direction of wave propagation. The particle motion lies on the same line as the energy travel.

3.4.5 How Sound Waves Propagate

• Compression: When the source moves forward it pushes neighbouring particles together, producing a region of higher pressure.
• Rarefaction: When the source moves back it leaves a region of lower pressure.
• These compressions and rarefactions travel through the medium, carrying the acoustic energy.

3.4.6 Key Features of Longitudinal Sound Waves

• Particle displacement is parallel to the direction of wave travel.
• Energy is transmitted via successive compressions and rarefactions.
• Can travel through any compressible material (gases, liquids, solids).
• The speed of sound depends on the medium’s elasticity and density.

3.4.7 Speed of Sound

The general expression is

\$v = \sqrt{\frac{B}{\rho}}\$

where B is the bulk modulus (elasticity) and ρ is the density of the medium.

In dry air at 20 °C the speed is ≈ 340 m s⁻¹ (the syllabus gives a range of 330 – 350 m s⁻¹**). The value changes with temperature because both B and ρ vary.

3.4.8 Measuring the Speed of Sound in Air

Two methods commonly used at IGCSE level are:

1. Resonance (standing‑wave) method

   • Set up a closed tube of known length L with a speaker at one end.
   • Adjust the speaker frequency until a resonance (loud maximum) is observed.
   • At the first resonance the tube length equals one‑quarter of the wavelength:
       L = λ/4 → λ = 4L.
   • Measure the frequency f with a calibrated frequency counter.
   • Calculate the speed:
       v = f λ = 4 f L.

2. Time‑of‑flight (echo) method

   • Place a loudspeaker and a microphone a known distance d apart.
   • Emit a short pulse and record the time interval Δt between the direct signal and its echo from a distant wall.
   • Speed of sound:
       v = 2d / Δt (the pulse travels to the wall and back).

3.4.9 Comparison with Transverse Waves

3.4.10 Mathematical Description of a Simple Harmonic Sound Wave

The displacement s of a particle in a sinusoidal sound wave is

\$s(x,t)=s_{\max}\,\sin\!\bigl(kx-\omega t\bigr)\$

• s_max – amplitude of particle displacement
• k = 2\pi/\lambda – wave number
• ω = 2\pi f – angular frequency
• λ – wavelength
• f – frequency

3.4.11 Why Sound Is Perceived as a Longitudinal Wave

1. The eardrum responds to rapid pressure changes caused by compressions and rarefactions.
2. These pressure variations make the eardrum vibrate back‑and‑forth, reproducing the longitudinal particle motion of the incident wave.
3. The brain interprets the vibration frequency as pitch and the amplitude as loudness.

3.4.12 Common Misconceptions

• “Sound travels like a ripple on water.” – Surface ripples are transverse waves; sound in water is longitudinal.
• “The air itself moves from the source to the listener.” – Air particles only oscillate about fixed positions; the pressure disturbance propagates.
• “Sound can travel in a vacuum.” – No medium → no compression → no sound.

3.4.13 Summary

Sound waves are longitudinal because the particles of the medium vibrate in the same direction that the wave travels. This produces alternating compressions and rarefactions that convey acoustic energy through gases, liquids and solids. Understanding the longitudinal nature of sound explains why a material medium is essential, how the speed of sound depends on elasticity and density, and how we can measure that speed in the laboratory.