Two tuning forks emit sinusoidal sound waves of nearly equal frequencies in air

PHYSICS · Multi-part · A Level · Physics · Waves · Waves

Problem

Two tuning forks emit sinusoidal sound waves of nearly equal frequencies in air. A student wishes to study the waxing and waning of loudness when the forks are sounded together. (i) Define the term beat frequency. (ii) Taking the particle displacements produced by the two forks to be

y_1=A\,\sin(2\pi f_1 t)

and

y_2=A\,\sin(2\pi f_2 t)

with

f_2=f_1+\Delta f\;(\Delta f\ll f_1)

, derive an expression for the resultant displacement and hence obtain the relation for the beat frequency. (iii) The two forks have frequencies

256\,\text{Hz}

and

260\,\text{Hz}

. How many maxima of sound intensity will the student hear in

15\,\text{s}

Related theory

Wave Superposition
Beats
Waves
Interference

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