First slide

Beats

Question

The frequencies of two sound sources are 256 Hz and 260 Hz. At t = 0, the intensity of sound is maximum. Then the phase difference at the time t = 1/16 sec will be

Moderate

A

Zero
B

$π$
C

$π / 2$
D

$π / 4$

Solution

Time interval between two consecutive beats
$T = \frac{1}{n_{1} - n_{2}} = \frac{1}{260 - 256} = \frac{1}{4} \sec$ so, $t = \frac{1}{16} = \frac{T}{4} \sec$
By using time difference = $\frac{T}{2 π} \times$ Phase difference
$\Rightarrow \frac{T}{4} = \frac{T}{2 π} \times φ \Rightarrow φ = \frac{π}{2}$

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