Question

The ratio of two wavelengths of sound in air is 3:4. Find the ratio of their frequencies.

Answer 1

Step 1- Given data

$\frac{{\lambda }_1}{{\lambda }_2}=\frac{3}{4}$.

$v={\lambda }^{}f$, where the wave velocity is $v$, frequency is $f$, and wavelength is $\lambda$.

So, $\lambda =\frac{v}{f}$.

Step 2-To find the ratio of frequencies-

For constant speed, $\frac{{\lambda }_1}{{\lambda }_2}=\frac{f_2}{f_1}$.

So, $\frac{{\lambda }_1}{{\lambda }_2}=\frac{3}{4}=\frac{f_2}{f_1}$.

Thus, $\frac{f_1}{f_2}$$=$$\frac{4}{3}$.

Hence, the ratio of their frequencies is 4:3.