Question

The wavelength of two sound wave in air are $\frac{81}{173}$ m and $\frac{81}{170}$ m. They produce $10$ beats per second. Calculate the velocity of sound in air

Answer 1

Given,

Beat =$10beat/s$

$|f_1-f_2|=10$

$|\frac{v}{{\lambda }_1}-\frac{v}{{\lambda }_2}|=10$

$v=10\left|\frac{{\lambda }_1{\lambda }_2}{{\lambda }_2-{\lambda }_1}\right|=10\left|\frac{\frac{81}{173}\times \frac{81}{170}}{\frac{81}{170}-\frac{81}{173}}\right|=270m{s}^{-1}$

Hence, velocity of sound in air $270m{s}^{-1}$