The longitudinal displacement of a mass element in a medium as a sound wave passes through it is given by s = sm cos (kx – ωt). Consider a sound wave of frequency 384 Hz and wavelength 0.55 m. If sm = 14 µm, what is the displacement of an element of air located at x = 2.4 m at time t = 6.7 ms?

The longitudinal displacement is 1.373x10⁻⁵m

Explanation:

Given:

f = 384 Hz

λ = 0.55 m

x = 2.4 m

t = 6.7 ms = 6.7x10⁻³s

sm = 14 µm = 14x10⁻⁶m

According the question, the displacement is:

But:

Replacing:

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the area between the graph and the t axis