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Concepts Of Physics MCQ Edition [Volume 1]
Exam
Concepts Of Physics MCQ Edition [Volume 1]
Subject
Physics
Chapter
Sound Waves

Concepts Of Physics MCQ Edition [Volume 1] · Physics · Sound Waves

Which of the following expressions best describes the sound...

Which of the following expressions best describes the sound produced when we clap our hands?
Here, pp indicates the change in pressure from the equilibrium value.

Options

  1. Ap=p0sin⁡kxcos⁡ωtp = p_0 \sin kx \cos \omega t
  2. Bp=Σ p0nsin⁡(knx−ωnt)p = \Sigma\, p_{0n} \sin(k_n x - \omega_n t)
  3. Cp=p0cos⁡kxsin⁡ωtp = p_0 \cos kx \sin \omega t
  4. Dp=p0sin⁡(kx−ωt)p = p_0 \sin(kx - \omega t)

Correct answer

B. p=Σ p0nsin⁡(knx−ωnt)p = \Sigma\, p_{0n} \sin(k_n x - \omega_n t)

Step-by-step solution

A clap produces a sound pulse, which is a complex, non-periodic wave.

According to Fourier's theorem, any complex wave or pulse can be expressed as a superposition of many simple harmonic waves of different frequencies, amplitudes, and wavelengths.

Therefore, the sound of a clap is best described by the sum of multiple travelling waves, given by p=Σ p0nsin⁡(knx−ωnt)p = \Sigma\, p_{0n} \sin(k_n x - \omega_n t).

Options (1) and (3) represent standing waves, while option (4) represents a single harmonic travelling wave (a pure tone).
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