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Differential Equation of Wave

A wave has ...

Question

A wave has $S H M$ whose period is $4 s$ while another wave which also posses $S H M$ has its period $3 s$ . If both are combined, then the resultant wave will have the period equal to

A

4 s

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B

5 s

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C

12 s

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D

3.43 s

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Solution

The correct option is B $12 s$
$T_{1} = 3 s e v T_{2} = 4 S e c$
When two waves of independent frequency are superimposed then beat will be formed,
Beat frequency $f_{b} = f_{1} - f_{2} = 1 / T_{1} - 1 / T_{2} = 1 / 3 - 1 / 4 = 1 / 12$
$T_{b} = 1 / f_{b} = 12$ sec

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