Two waves of lengths 50 ; cm and 51 ; cm prod | vedclass

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(A) The frequency of a wave is given by $n = \frac{v}{\lambda}$,where $v$ is the velocity and $\lambda$ is the wavelength.Given wavelengths are $\lamb

Vedclass · Accepted Answer

$306$

Vedclass · Answer

(A) The frequency of a wave is given by $n = \frac{v}{\lambda}$,where $v$ is the velocity and $\lambda$ is the wavelength.Given wavelengths are $\lambda_1 = 50 \; cm = 0.50 \; m$ and $\lambda_2 = 51 \; cm = 0.51 \; m$.The frequencies are $n_1 = \frac{v}{0.50}$ and $n_2 = \frac{v}{0.51}$.The beat frequency is the difference between the two frequencies: $\Delta n = n_1 - n_2 = 12 \; Hz$.Substituting the values: $v \left( \frac{1}{0.50} - \frac{1}{0.51} ight) = 12$.$v \left( \frac{0.51 - 0.50}{0.50 	imes 0.51} ight) = 12$.$v \left( \frac{0.01}{0.255} ight) = 12$.$v = \frac{12 	imes 0.255}{0.01} = 12 	imes 25.5 = 306 \; m/s$.

Two waves of lengths $50 \; cm$ and $51 \; cm$ produce $12$ beats per second. The velocity of sound is .... $m/s$.

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