Question

A fire engine is rapidly approaching you at a stop light. What happens to the frequency and pitch of the sound as the fire engine draws closer? The frequency increases, and the pitch decreases The frequency increases, and the pitch increases The frequency decreases, and the pitch decreases The frequency decreases, and the pitch increases

Answer 1

Answer:

The frequency increases, and the pitch increases

Explanation:

• Doppler's law of sound is applicable in such case when the observer or the sound source or both are moving relative to each other.

• In such a case due to space-time constraint the waveform of the sound adjust themselves so as to obey the law of conservation of energy.

The apparent frequency of the sound for the observer is given by:

$f_o=(\frac{s+v_o}{s+v_s} )f$ ....................................(1)

where:

$f_o=$ observed frequency

$f=$ original source frequency

$s=$ speed of sound

$v_s=$ speed of source relative to the observer (taken negative when approaching towards the observer and vice-versa)

$v_o=$ speed of observer relative to the source (taken negative when moving away from the source and vice-versa)

According to the given situation, eq. (1) becomes:

$f_o=(\frac{s}{s-v_s} )f$

Since, $\frac{s}{s-v_s} >1$

Therefore

$f_o>f$

Pitch is very closely related to the frequency, it means that how fast is the amplitude of sound varying with time.