Question

Two waves of wavelengths 50cm and 51 cm produced 12 beats per sec. The velocity of sound is

1- 340m/s 2- 331 m /s

3- 306m/s 4- 360m/s

Answer 1

Given,
$$\begin{gathered} \mathrm{Wavelengths}, \\ {\mathrm{\lambda }}_1=50\mathrm{cm}=0.5\mathrm{m} \\ {\mathrm{\lambda }}_2=51\mathrm{cm}=0.51\mathrm{m} \\ \mathrm{frequency}\mathrm{of}\mathrm{beats},\mathrm{f}=12 \\ \mathrm{Now}, \\ \mathrm{Frequency}\mathrm{of}\mathrm{beats}, \\ \mathrm{f}=\frac{\mathrm{v}}{{\mathrm{\lambda }}_1}-\frac{\mathrm{v}}{{\mathrm{\lambda }}_2}=\mathrm{v}[\frac{1}{{\mathrm{\lambda }}_1}-\frac{1}{{\mathrm{\lambda }}_2}] \\ 12=\mathrm{v}[\frac{1}{0.5}-\frac{1}{0.51}] \\ \mathrm{or}\mathrm{v}=306\mathrm{m}/\mathrm{s} \end{gathered}$$