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Question

Three sound waves of equal amplitudes have frequencies $$(\mathrm{v}-1),\ \mathrm{v},\ (\mathrm{v}+1)$$. They superpose to give beats. The number of beats produced per second will be 


A
4
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B
3
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C
2
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D
1
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Solution

The correct option is C $$2$$
$$\mathrm{p}_{1}=\mathrm{p}_{0}\sin 2\pi(\mathrm{x}-1)\mathrm{t} \mathrm{p}_{2}=\mathrm{p}_{0}\sin 2\pi(\mathrm{x})\mathrm{t} \mathrm{p}_{3}=\mathrm{p}_{0}\sin 2\pi(\mathrm{x}+1)\mathrm{t} \mathrm{p}=\mathrm{p}_{1}+\mathrm{p}_{3}+\mathrm{p}_{2}$$
      $$=\mathrm{p}_{0}\sin 2\pi(\mathrm{x}-1)\mathrm{t}+\mathrm{p}_{0}\sin 2\pi(\mathrm{x}+1)\mathrm{t}+\mathrm{p}_{0}\sin 2\pi \mathrm{x}\mathrm{t}$$
      $$=2\mathrm{p}_{0}\sin 2\pi \mathrm{x}\mathrm{t}\cos 2\pi \mathrm{t}+\mathrm{p}_{0}\sin 2\pi \mathrm{x}\mathrm{t} =\mathrm{p}_{0}\sin 2\pi \mathrm{x}\mathrm{t}[2\cos\pi \mathrm{t}+1]$$
$$f_{beat}=2$$

Physics

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