## Question

Two sounding bodies producing progressive waves given by

are situated very near to the ears of a person who will hear

### Solution

2 beats per second with intensity ratio 49/1between maxima and minima.

The two amplitude of the two sounds are *a*_{1} = 4 units and *a*_{2} = 3 units. Their angular frequencies are ω_{1} = 400 π rad s^{–1} and ω_{2} = 404 π rad s^{–1}. Therefore, their frequencies are *V*_{1} = 200 Hz and *V*_{2} = 202 Hz. Hence the beat frequency = *V*_{2} – *V*_{1} = 2 Hz, i.e. the person will hear 2 beats per second. The intensity ratio is given by

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