(a) State the three characteristics of sound and the factor on which each of them depends. (b) Explain resonance as applied to sound. (c) What role does ech...

(a) Three characteristics of sound and their dependence

• Pitch depends on the frequency of the sound wave.
• Loudness depends on the amplitude (intensity) of the sound wave.
• Quality (timbre) depends on the number and relative amplitudes of the overtones (harmonics) present, i.e. the waveform.

(b) Resonance

Resonance in sound occurs when a body is set into vibration with large amplitude because it is acted on by a periodic force whose frequency equals the body's own natural frequency of vibration. At this matching frequency the body absorbs energy most effectively and vibrates strongly.

(c) Role of echo in concert-hall construction

Echoes (reflections of sound) must be controlled so that reflected sound does not arrive so late as to blur speech and music (excessive reverberation) nor die away too quickly. Sound-absorbing materials and suitably shaped, angled surfaces are used so that reverberation time is correct and the sound is spread evenly, giving good acoustics throughout the hall.

(d) The ear drum

Data: \(r = 2.1\text{ mm} = 2.1\times10^{-3}\text{ m}\), amplitude \(A = 0.8\times10^{-7}\text{ m}\), \(f = 2400\text{ Hz}\), pressure change \(p = 3.6\times10^{-5}\ \text{N m}^{-2}\), \(\pi = 3.14\).

(i) Period: \(T = \dfrac{1}{f} = \dfrac{1}{2400} = 4.17\times10^{-4}\ \text{s}\).

(ii) Maximum velocity: \(v = \omega A = 2\pi f A = 2\times3.14\times2400\times0.8\times10^{-7}\).

\(v = 15072 \times 0.8\times10^{-7} = 1.21\times10^{-3}\ \text{m s}^{-1}\).

(iii) Maximum acceleration: \(a = \omega^{2}A = (2\pi f)^{2}A = (15072)^{2}\times0.8\times10^{-7}\).

\(a = 2.27\times10^{8}\times0.8\times10^{-7} = 18.2\ \text{m s}^{-2}\).

(iv) Force: area of ear drum \(A_{d} = \pi r^{2} = 3.14\times(2.1\times10^{-3})^{2} = 1.39\times10^{-5}\ \text{m}^{2}\).

\(F = p \times A_{d} = 3.6\times10^{-5}\times1.39\times10^{-5} = 5.0\times10^{-10}\ \text{N}\).