Question

Two sound waves of wavelengths 40 cm and 40.5 cm produce 10 beats per second. What will be the speed of sound in air?

Answer 1

given

two Sound waves of wavelengths

$40cm\to 0.4m$

$40.5cm\to 0.45m$

formed $10$ beats in $1$ second

let the speed of sound be ${}^{\prime }{v}^{\prime }$ beat frequency $=\frac{10}{1}=10Hz$

but

beat frequency $=|f_1-f_2|\to \left(2\right)$

Since $f_{\lambda }=v\to$

$\begin{array}{ccc}\begin{array}{c}{f}_1=\frac{v}{0.4}\\ f_2=\frac{v}{0.45}\end{array}\}& \to & |\frac{v}{0.4}-\frac{v}{0.45}|\end{array}=10$

$2.5v-2.4v=10$

$V=100m/s$