The sound waves of wavelengths 5 ~m and 6 ~m | vedclass

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Question

(A) Given wavelengths are $\lambda_1 = 5 ~m$ and $\lambda_2 = 6 ~m$.Let the velocity of sound be $v$.The frequencies of the two waves are $n_1 = \frac

Vedclass · Accepted Answer

$300$

Vedclass · Answer

(A) Given wavelengths are $\lambda_1 = 5 ~m$ and $\lambda_2 = 6 ~m$.Let the velocity of sound be $v$.The frequencies of the two waves are $n_1 = \frac{v}{\lambda_1} = \frac{v}{5}$ and $n_2 = \frac{v}{\lambda_2} = \frac{v}{6}$.The number of beats produced in $3 ~s$ is $30$,so the beat frequency is $f_{beat} = \frac{30}{3} = 10 ~Hz$.The beat frequency is the difference between the two frequencies: $n_1 - n_2 = 10$.Substituting the values: $\frac{v}{5} - \frac{v}{6} = 10$.Taking the common denominator: $v \left( \frac{6 - 5}{30} \right) = 10$.$v \left( \frac{1}{30} \right) = 10$.Therefore,$v = 300 ~m/s$.

The sound waves of wavelengths $5 ~m$ and $6 ~m$ produce $30$ beats in $3 ~s$. The velocity of sound is: (in $~m/s$)

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