Two tuning forks have frequencies 380 and 384 hertz...

Two tuning forks have frequencies 380 and 384 hertz respectively. When they are sounded together, they produce 4 beats. After hearing the maximum sound, how long will it take to hear the minimum sound [MP PMT/PET 1998] (a) $1 / 2 \mathrm{sec}$ (b) $1 / 4 \mathrm{sec}$ (c) $1 / 8 \mathrm{sec}$ (d) $1 / 16 \mathrm{sec}$

Two tuning forks have frequencies 380 and 384 hertz respectively. When they are sounded together, they produce 4 beats. After hearing the maximum sound, how long will it take to hear the minimum sound [MP PMT/PET 1998]
(a) $1 / 2 \mathrm{sec}$
(b) $1 / 4 \mathrm{sec}$
(c) $1 / 8 \mathrm{sec}$
(d) $1 / 16 \mathrm{sec}$

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Key Concepts

Beat Frequency

Beat frequency is the number of beats per second produced when two waves of nearly identical frequencies interfere. It is defined as the absolute difference between the two frequencies and dictates how fast the amplitude of the resultant wave oscillates between maximum and minimum values.

Amplitude Modulation in Beats

Amplitude modulation in the context of beats refers to the periodic variation in the loudness of sound resulting from the interference of two waves. The alternating constructive and destructive interference produces a modulated amplitude envelope where the sound cyclically reaches maximum and minimum intensities.

Time Interval Between Maximum and Minimum Amplitude

In the phenomenon of beats, the time between a maximum (loud sound) and the subsequent minimum (soft sound) is directly related to the frequency difference of the two superposed waves. Specifically, since the overall beat period is the reciprocal of the beat frequency, the interval between a maximum and a minimum is half of that beat period.

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