Question

The ratio of frequencies of two waves traveling through the same medium is $2:5$. The ratio of their wavelengths will be

• A. $2:5$
• B. $5:2$
• C. $3:5$
• D. $5:3$

Answer 1

The correct option is B

$5:2$

Step 1: Given data

The ratio of frequencies$\left(f_1:f_2\right)=2:5$

Step 2: Formula used

As we now that the wave speed is equal to the product of its frequency and wavelength.

Thus, the relationship between wavelength and frequency is described by the following equation:

$f=\frac{v}{\lambda }·····\left(1\right)$

Where $f=$frequency, $\lambda =$wavelength, and $v=$wave velocity

From the equation $\left(1\right)$, it is clear that frequency and wavelength have an inverse relationship.then,

$$\begin{gathered} f\propto \frac{1}{\lambda } \\ \frac{f_1}{f_2}=\frac{{\lambda }_2}{{\lambda }_1} \end{gathered}$$

Step 3: Compute the ratio of wavelength

Substitute the known values in the formula,

$$\begin{gathered} \frac{2}{5}=\frac{{\lambda }_2}{{\lambda }_1} \\ \frac{{\lambda }_1}{{\lambda }_2}=\frac{5}{2} \\ {\lambda }_1:{\lambda }_2=5:2 \end{gathered}$$

Thus, the ratio of wavelength would be $5:2$.

Hence, option B is the correct answer.