Question

Two cars moving in opposite directions approach each other with speeds of 22m/s and 16.5m/s respectively. The driver of the first car blows a horn having a frequency 400Hz. The frequency heard by the driver of the second car is [velocity of sound 340m/s]:
A. 448 Hz
B. 350 Hz
C. 361 Hz
D. 441 Hz

Answer 1

Hint: The number of occurrences of repeating events at a regular interval of time is known as Frequency. It is measured in Hertz which is equal to one occurrence of a repeating event per second.

Complete step by step answer:
Given,
\[f' = \left( {\nu - {\nu _ \circ }} \right)\aleph f\]
\[{f_1} = 400Hz\]
\[{\nu _s} = 340m/s\]

We know that when both the source and observer are moving towards each other
\[{f_2} = \left( {\dfrac{{{\nu _s} - {v_1}}}{{{\nu _s} + {\nu _1}}}} \right)\]
\[\left( {\dfrac{{340 + 16.5}}{{340 - 22}}} \right) \times 400\]
\[\left( {\dfrac{{340 + 16.5}}{{340 - 22}}} \right) \times 400\]\[ = 448Hz\]
Thus, the correct answer to the given question is option (A).

Additional information:
The Doppler Effect is the probable difference in frequency because of the relative motion between the observer and source.
The Doppler Effect causes a difference in the wavelength and frequency of the wave. The probable change of the wavelength can be determined using the formula:
\[{H_{apparent}} = \dfrac{{{h_s} - {\nu _s}}}{{{n_ \circ }}}\]
If the source is advancing towards the observer, but the observer shifts away from the source or vice versa, the apparent wavelength can be determined by
\[{H_{apparent}} = \dfrac{{\nu - {\nu _s}}}{{\nu .{h_s}}}\]

If the source is shifting away from the observer and the observer advances towards the source or vice versa, the apparent wavelength of can be determined by
\[{H_{apparent}} = \dfrac{{\nu + {\nu _s}}}{{\nu .{h_s}}}\]

Doppler Effect changes the frequency of the wave anticipated by the observer. The emitted frequency and the apparent frequency are related to each other. The apparent frequency can be calculated by
If both the source and observer move towards each other, the apparent frequency will increase, whereas if the source and observer move away from each other, the apparent frequency falls.
If the source or observer are accelerated bodies, the speed of the source at the time the wave was emitted and the speed of the observer at the time of receiving the sound is taken into consideration.

Note: In the above question, both source and observer advance towards each other. Hence, the apparent frequency will increase.