A airplane is approaching you at a speed of 360km/h. If you measure the pitch of its approaching engines to be 512 Hz, what must be the actual frequency of the sound of the engines? The speed of sound in air is 345m/s

answer is 364Hz please explain steps?

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To determine the actual frequency of the sound of the engines, we can use the concept of the Doppler effect. The Doppler effect describes the perceived change in frequency of a sound wave when there is relative motion between the source of the sound and an observer.

Here's how we can calculate the actual frequency of the sound of the engines:

1. Firstly, we need to determine the relative velocity between the source (the airplane) and the observer (you). In this case, the airplane is approaching you, so the relative velocity is the sum of the airplane's speed and your speed: 360 km/h.

2. We need to convert the relative velocity into meters per second, as the speed of sound is given in meters per second. Since 1 kilometer is equal to 1000 meters and 1 hour is equal to 3600 seconds, we can convert the relative velocity: 360 km/h = (360 * 1000) / 3600 = 100 m/s.

3. Now, we can apply the formula for the Doppler effect:

Actual Frequency = Source Frequency * (Speed of Sound + Observer's Velocity) / (Speed of Sound + Source's Velocity)

In this case:
Source Frequency = 512 Hz
Speed of Sound = 345 m/s
Observer's Velocity = 0 m/s (since you are not moving)
Source's Velocity = -100 m/s (negative because the source is approaching you)

4. Substituting these values into the formula:

Actual Frequency = 512 Hz * (345 m/s + 0 m/s) / (345 m/s - 100 m/s)
Actual Frequency = 512 Hz * 345 m/s / 245 m/s
Actual Frequency = 364 Hz

Therefore, the actual frequency of the sound of the engines would be 364 Hz.

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