The longitudinal displacement of a mass element in a medium as a sound wave passes through it is given by s = s_m cos (kx - ωt).Consider a sound wave of frequency 440 Hz and wavelength 0.75m.If s_m = 12 µm, how long does it take an element of air to move from a displacement of 12 µm to a displacement of 0 µm? A)0.57 ms B)1.1 ms C)2.3 ms D)3.4 ms E)4.6 ms

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Quizplus · Accepted Answer

The displacement s = s_m cos (kx - ωt) reaches 0 µm when cos (kx - ωt) = 0. This occurs at ωt = π/2. The angular frequency ω = 2πf = 2π(440 Hz). The time taken is t = (π/2) / ω = (π/2) / (2π * 440) = 1/(4 * 440) = 0.57 ms.

The Longitudinal Displacement of a Mass Element in a Medium