Shake it to my Beats

Classical Mechanics Level 4

A car is moving towards a wall with a velocity = $10 \text{ m/s}$ . The car blows it's horn at a frequency of $240 \text{ Hz}$ . A man is poking his head out of the car at that time too. If the speed of sound in air is $330 \text{ m/s}$ , then what will be the frequency at which he will hear the beats?

Note:- Ignore the human hearing range.

The answer is 15.

2 solutions

Kunal Verma
Mar 1, 2016

Assuming the wall to be an observer and the car to be the source, the frequency of the sound received by observer will be = $\frac{f \times c}{c \ - \ v} \ = \ f1 \ (say)$ by Doppler Effect where $f$ is the frequency of sound emitted by the car, $c$ is speed of sound in air and $v$ is the speed of the car.

Now assuming the man to be the observer and the wall to be the source ( frequency remains constant after reflection of wave from the wall).

Frequency of sound heard by the man = $\frac{ f1 \times ( \ c \ + \ v \ )}{c} \ = \frac{f \times ( \ c \ + \ v \ )}{ c \ - \ v \ } \ = \ f2 \ (say)$

The beat frequency = $f2 \ - \ f$ ( as the sound wave spreads in all directions, he will initially hear the car's sound too) = $\frac{2 \times f \times v}{ c \ - \ v} \ = \boxed{15}$ .

(Theoritically)

Practically, human ears cant sense more than 10 beats/s

Md Zuhair - 3 years, 4 months ago

Varun Raj
Apr 22, 2016

The human ear cannot hear more than one 10 beats a second so answer should be 0 beats

Yes but that's something we have ignored here. I will make that clear in the question. In future though, please post your reports under the report section.

Kunal Verma - 5 years, 1 month ago

Shake it to my Beats

The answer is 15.

2 solutions

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