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Sound Waves

Part of the WAEC WASSCE study roadmap. Physics topic phy-9 of Physics.

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Sound Waves

🟢 Lite — Quick Review (1h–1d)

Rapid summary for last-minute revision before your exam.

Sound is a longitudinal mechanical wave: particles of the medium vibrate parallel to the direction of wave travel, producing alternating compressions (high-pressure regions) and rarefactions (low-pressure regions). It needs a material medium — demonstrated in WAEC by the bell-jar experiment showing the ringing becomes inaudible as air is pumped out.

The two essential formulas are v = fλ (wave speed = frequency × wavelength) and v = √(E/ρ) for solids. For air at 0 °C, v ≈ 331 m s⁻¹; it rises by roughly 0.6 m s⁻¹ per °C. The audible range is 20 Hz to 20 kHz; ultrasonic imaging and SONAR exploit frequencies above this.

Quick traps: pitch depends on frequency, not amplitude; the minimum echo distance in air is ~17 m because the ear retains a sound for about 0.1 s.

🟡 Standard — Regular Study (2d–2mo)

Standard content for students with a few days to months.

Nature and Properties

A sound wave is a longitudinal mechanical wave — mechanical because it requires a medium (solids, liquids, or gases), longitudinal because oscillation of particles is along the direction of propagation. A vibrating source (e.g. tuning fork prong) pushes nearby air molecules forward, compressing them; when the prong swings back, a rarefaction forms. These pressure disturbances travel outward at the speed of sound, while individual air molecules only oscillate about fixed positions.

Speed of Sound in Different Media

MediumTypical speed (m s⁻¹)Reason
Air (0 °C)331Low elasticity, low density
Air (20 °C)~343Increases with √T
Water~1480Higher bulk modulus
Steel~5000–6000High Young modulus E

The governing expressions are v = √(E/ρ) for a solid rod (E = Young modulus, ρ = density) and v = √(γP/ρ) for a gas (γ = ratio of specific heat capacities, P = pressure, ρ = gas density).

Pitch, Loudness and Quality

  • Pitch — set by the frequency of the wave; a 256 Hz tuning fork sounds lower than a 512 Hz one.
  • Loudness — related to amplitude (or intensity I = P/A, with units W m⁻²). Because the ear responds logarithmically, the intensity level in decibels is β = 10 log(I/I₀), with reference I₀ = 10⁻¹² W m⁻².
  • Quality (timbre) — what distinguishes a violin from a piano playing the same note; depends on the harmonics and overtones present above the fundamental frequency.

Reflection of Sound: Echoes and Reverberation

An echo is a reflected sound heard distinctly. Because the human ear retains a sensation for ≈ 0.1 s, the reflected wave must arrive at least 0.1 s later. With v ≈ 340 m s⁻¹, the minimum distance to a reflector is d = vt/2 ≈ 17 m. Reverberation is the persistence of multiple overlapping reflections in enclosed halls.

🔴 Extended — Deep Study (3mo+)

Comprehensive coverage for students on a longer study timeline.

Beyond Human Hearing

Infrasonics (f < 20 Hz) are produced by earthquakes, volcanic eruptions and large machinery; elephants and whales use them. Ultrasonics (f > 20 kHz) are emitted by bats, dolphins, and quartz-crystal transducers. Applications:

  • SONAR on ships: depth d = vt/2, with t measured for the pulse to return.
  • Medical ultrasonography: echoes from tissue boundaries are mapped to images.
  • Industrial flaw detection: cracks in metals reflect ultrasound before the main pulse returns.

Common Mistakes in WAEC WASSCE

  1. Confusing loudness (subjective, in decibels or phons) with intensity (objective, W m⁻²). Higher amplitude ⇒ greater intensity ⇒ perceived as louder, but the relationship is non-linear.
  2. Writing the speed of sound in air as 3 × 10⁸ m s⁻¹ — that is the speed of light. Common error when students rush the formula v = fλ and muddle constants.
  3. Saying pitch depends on amplitude. Doubling amplitude makes a note louder, not higher.
  4. Forgetting temperature’s effect: cold morning air at 10 °C carries sound at ~337 m s⁻¹, not 343.
  5. Stating echo minimum distance as 34 m — that is the total round trip; the distance to the wall is half.

Practice Prompts

  1. A ship’s SONAR emits a 40 kHz pulse and receives the echo from a shoal of fish 600 m away in sea water (v = 1500 m s⁻¹). Calculate the time delay between transmission and reception, and the wavelength of the pulse in water.
  2. A factory siren produces 90 dB at 10 m from its source. By what factor must your distance increase so that the intensity level falls to 60 dB? (Hint: intensity obeys the inverse-square law in free space; a 30 dB drop means I decreases by a factor of 10³ = 1000, so distance multiplies by √1000 ≈ 31.6.)

Linkage to Adjacent Topics

Sound waves connect to stationary (standing) waves in pipes and strings (end correction, harmonics on open/closed tubes), to Doppler effect (frequency shift when source or observer moves), and to electromagnetic waves as a contrast: EM waves are transverse and need no medium, while sound is longitudinal and does.

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