Physics

Problem

A sound wave travelling in air is given by

s(x,t)=0.10\,\text{Pa}\,\cos(kx-\omega t+\tfrac{\pi}{6})

. A detector is placed at

x=0

. a. (i) Obtain an expression for the instantaneous phase of the air element at the detector as a function of time. b. (ii) Derive a general expression for the time

\Delta t

taken by this air element to change its phase from an initial value

\phi_1

to a later value

\phi_2

. c. (iii) Using the result of part (ii), calculate the shortest time in which the phase at the detector changes from

\tfrac{\pi}{6}

\tfrac{11\pi}{6}

if the frequency of the wave is

440\,\text{Hz}

. Explain each step of your reasoning.

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