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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 differance at the time t = 1/16 sec will be 


A
Zero
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B
π
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C
π/2
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D
π/4
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Solution

The correct option is D $$ \pi/4 $$

Given,

Frequency $${{f}_{1}}\ \And \ {{f}_{2}}\ =\ 260\ Hz\ \And \ 256\ Hz$$

Phase difference for two consecutive beats is $$\pi $$.

Beat frequency $${{f}_{b}}=\left| {{f}_{1}}-{{f}_{2}} \right|=260-256=4\,Hz$$, four beat per second.

Frequency of temporal interference is $$f=\dfrac{\left| {{f}_{1}}-{{f}_{2}} \right|}{2}=2\,Hz$$

Phase difference $$\delta \left( t=\dfrac{1}{16}\sec  \right)$$,    $$\delta =2\pi f\times t=2\pi \times 2\times \dfrac{1}{16}=\dfrac{\pi }{4}$$


Physics

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