Question 284: Waves

Question

When source of sound moves towards a stationary observer, the apparent frequency heard by him

Accepted Answer

When a source of sound moves towards a stationary observer, the Doppler effect takes place.
According to the NCERT formula:
If the source moves towards a stationary observer, the apparent frequency $f'$ heard by the observer is:
$$ f' = \frac{v}{v - v_s} f $$
where,
$f$ = actual frequency of the source
$v$ = speed of sound in air
$v_s$ = speed of the source towards the observer
Step-by-step reasoning:
Since the denominator $v - v_s$ is less than $v$, $f' > f$.
$\implies$ The apparent frequency
increases
.
The wavelength $\lambda'$ of the sound received by the observer is
$$\lambda' = \frac{v - v_s}{f}$$
Since $v_s$ is positive (source moves towards observer), $v - v_s < v$, hence $\lambda' < \lambda$ (where $\lambda = \frac{v}{f}$).
$\implies$
Wavelength decreases
.
Correct option:
Option B: increases while wavelength decreases.

Answer

increases and wavelength also increases.

Answer

increases while wavelength decreases.

Answer

remains the same while wavelength decreases.

Answer

decreases and wavelength remains the same.

Waves

When source of sound moves towards a stationary observer, the apparent frequency heard by him

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