Question

Two waves propagating in the same medium have wavelengths in the ratio of 1:4. What is the ratio of their frequencies?

• A. 1:4
• B. 4:1
• C. 1:2
• D. 2:1

Answer 1

The correct option is B 4:1

The ratio of wavelengths = 1:4
We know that,
$v=f\times \lambda$,
where $v=$ Velocity of sound,
$\lambda =$ Wavelength of the sound, and
$f$ = Frequency.

Since, both the waves travel in the same medium, $v$ remains constant.
${\lambda }_1\times f_1={\lambda }_2\times f_2$
$\Rightarrow \frac{{\lambda }_1}{{\lambda }_2}=\frac{f_2}{f_1}$

Given that $\frac{{\lambda }_1}{{\lambda }_2}=\frac{1}{4}$.
Hence, $\frac{f_2}{f_1}=\frac{1}{4}$ or
$\frac{f_1}{f_2}=\frac{4}{1}$
Thus, the ratio of frequencies of the two waves is 4:1.