Question

When both the listener and the source are moving towards each other, then which of the following is true regarding frequency and wavelength of the wave observed by the observer?

• A. more frequency, less wavelength.
• B. more frequency, more wavelength
• C. less frequency, less wavength.
• D. more frequency, constant wavelength.

Answer 1

The correct option is A

more frequency, less wavelength.

1. The change in the frequency of the sound due to the relative motion between the source and the listener is known as the Doppler effect.
2. The apparent frequency is given by, $f^{\text{'}}=f\left(\frac{v+v_0}{v-v_L}\right)$ where $v$ is the velocity of sound in air, $v_0$ is the velocity of the source, $v_L$and is the velocity of the listener and $f$ is the actual frequency.
3. When listener and source are moving towards each other, according to the sign conventions,$v_0$ is positive and $v_L$is also positive. Hence the apparent frequency increases
4. Since $f\propto \frac{1}{\lambda }$, $$\begin{gathered} f^{\text{'}}>f \\ \lambda >{\lambda }^{\text{'}} \end{gathered}$$ so the apparent wavelength decreases.

Therefore, Option A is the correct answer.