The wavelengths of two waves are 50 cm and 5 | vedclass

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(A) The speed of sound at $0^{\circ}C$ is $v_0 = 332 \ m/s$.The speed of sound at $t^{\circ}C$ is given by $v_t = v_0 + 0.61 	imes t$.At $t = 20^{\ci

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$14$

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(A) The speed of sound at $0^{\circ}C$ is $v_0 = 332 \ m/s$.The speed of sound at $t^{\circ}C$ is given by $v_t = v_0 + 0.61 	imes t$.At $t = 20^{\circ}C$,the speed of sound is $v_{20} = 332 + 0.61 	imes 20 = 332 + 12.2 = 344.2 \ m/s$.The frequencies of the two waves are $n_1 = \frac{v}{\lambda_1}$ and $n_2 = \frac{v}{\lambda_2}$.The number of beats produced per second is the difference in frequencies: $\Delta n = |n_1 - n_2| = v \left( \frac{1}{\lambda_1} - \frac{1}{\lambda_2} ight)$.Converting wavelengths to meters: $\lambda_1 = 0.50 \ m$ and $\lambda_2 = 0.51 \ m$.$\Delta n = 344.2 \left( \frac{1}{0.50} - \frac{1}{0.51} ight) = 344.2 \left( 2 - 1.96078 ight) = 344.2 	imes 0.03922 \approx 13.5 \approx 14 \ Hz$.

The wavelengths of two waves are $50 \ cm$ and $51 \ cm$ respectively. If the temperature of the room is $20^{\circ}C$,what will be the number of beats produced per second by these waves,given that the speed of sound at $0^{\circ}C$ is $332 \ m/s$?

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