A sound wave travelling in air is given by

PHYSICS · Multi-part · AP · Physics 2: Algebra-based · Waves Sound and Physical Optics · Waves Sound and Physical Optics

Problem

A sound wave travelling in air is given by s(x,t)=0.10 Pa cos⁡(kx−ωt+π6)s(x,t)=0.10\,\text{Pa}\,\cos(kx-\omega t+\tfrac{\pi}{6}). A detector is placed at x=0x=0. (i) Obtain an expression for the instantaneous phase of the air element at the detector as a function of time. (ii) Derive a general expression for the time Δt\Delta t taken by this air element to change its phase from an initial value ϕ1\phi_1 to a later value ϕ2\phi_2. (iii) Using the result of part (ii), calculate the shortest time in which the phase at the detector changes from π6\tfrac{\pi}{6} to 11π6\tfrac{11\pi}{6} if the frequency of the wave is 440 Hz440\,\text{Hz}. Explain each step of your reasoning.

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