A fire engine is moving at 40 m / s and sounding its horn. A car in front of the fire engine is

A fire engine is moving at 40 m / s and sounding its horn. A...

A fire engine is moving at $40 \mathrm{m} / \mathrm{s}$ and sounding its horn. A car in front of the fire engine is moving at $30 \mathrm{m} / \mathrm{s},$ and a van in front of the car is stationary. Which observer hears the fire engine's horn at a higher pitch, the driver of the car or the driver of the van?

Key Concepts

Doppler Effect

The Doppler Effect describes how the observed frequency of a wave changes when there is relative motion between the source of the wave and the observer. When the source and observer are moving towards each other, the observed frequency increases, resulting in a higher pitch for sound waves. Conversely, if they are moving apart, the frequency decreases, leading to a lower pitch.

Relative Motion

Relative motion is the concept of comparing the speeds and directions of the source and observer with respect to each other. In wave phenomena such as sound, the relative speeds directly affect the degree of frequency shift observed, as the effective velocity of the source or observer influences how wavefronts are received.

Transcript

00:01 So in this problem, we have a fire engine moving at 40 meters per second relative to the ground while he's sounding his horn.

00:09 So we'll draw our scenario.

00:12 We have a fire engine, and he's sounding his horn.

00:26 He's moving to the right, so we know the doll part effect will compress his waves to the in front of the fire engine.

00:35 And we know the fire engine is moving with a speed of 40 meters.

00:40 Per second relative to the ground to the right.

00:50 And we have a car in front of the fire engine, and the car is moving 30 meters per second to the right relative to the ground.

01:13 And then we also have a van in front of the car where the van is just stationary with respect to the ground.

01:25 So the van will be moving at zero meters per second relative to the ground here.

01:36 And so this is the setup.

01:41 The question is, does the driver of the car or the driver of the van hear a higher pitch from the fire engine's horn? well, what matters here is the relative velocity between the drivers and the fire engine.

02:03 Whatever one has the greater relative velocity, it will experience a greater doppler effect to the sound wave, and the sound wave in front of the fire engine will be more compressed and squeezed together to their perspective.

02:15 So the relative velocity of the fire engine with respect to the car, so i guess we'll call this, actually, sorry, we'll call this vf subcar for relative to the car.

02:34 And this is just going to be equal to the velocity of, or the speed of the fire engine minus the speed of the car, which we are given...

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