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Question

# One loudspeaker is producing a tone of frequency 236.30 Hz and a second loudspeaker a tone of frequency 236.50 Hz. What is the shortest time interval that you have to listen to the sound from the two loudspeakers to hear three beats?

Solution

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### 1 Concepts and Principles

1- $\textbf{Beat Frequency}$: A beat is a wave that results from the superposition of two waves of about the same frequency. The beat (the net wave) has a frequency equal to the average of the two frequencies and has variable amplitude. The frequency with which the amplitude of the net wave changes in called the beat frequency $f_{\text{beat}}$; it equals the difference in the frequencies of the two waves:

$\begin{gather*} f_{\text{beat}}=\abs{f_1-f_2}\tag{1} \end{gather*}$

2- The periodic time $T$ of a wave is related to its frequency of oscillation $f$ as follows:

$\begin{gather*} T=\dfrac{1}{f}\tag{2} \end{gather*}$

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