- #1

Lajka

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Hi,

this is a rather simple high-school assignment a friend asked me to help him, but I got kinda confused, and I'm sure someone will clarify it for me real quick.

A car is moving away from a rock with the speed [itex]v[/itex] and with the angle [itex]\alpha[/itex] from the rock. At the moment when the distance between the car and the rock is [itex]l[/itex], the car emmits a short sound wave. The speed of sound in the air is u.

What's the distance crossed till the driver in the car hears an echo?

So the picture is something like this

At moment [itex]t_{1} = \frac{l}{v \cdot sin(\alpha)}[/itex], the car will emit the sound wave with speed [itex]u[/itex]

It will take [itex]\Delta t=\frac{l}{u}[/itex] more time for the sound wave to reach the rock, and by then the car will have crossed [itex] s = v \cdot t_{2}[/itex]

where [itex]t_{2} = t_{1} + \Delta t[/itex]

But I'm stuck here. How exactly does a sound wave echo? If it just bounces back, it will miss the car of course, so does it perhaps reflect in some radial form? If it does, how should I calculate the point there the sound and the trajectory of the car intersect?

Of course, I think we can assume that [itex]v << u[/itex], otherwise there wouldn't be any point to any of this. Also disregard that the magnitudes of the arrows (like velocity, for instance) are different in the different pictures, I did it to make the pictures more clearer.

Thanks in advance.

this is a rather simple high-school assignment a friend asked me to help him, but I got kinda confused, and I'm sure someone will clarify it for me real quick.

**Homework Statement**A car is moving away from a rock with the speed [itex]v[/itex] and with the angle [itex]\alpha[/itex] from the rock. At the moment when the distance between the car and the rock is [itex]l[/itex], the car emmits a short sound wave. The speed of sound in the air is u.

What's the distance crossed till the driver in the car hears an echo?

**The attempt at a solution**So the picture is something like this

At moment [itex]t_{1} = \frac{l}{v \cdot sin(\alpha)}[/itex], the car will emit the sound wave with speed [itex]u[/itex]

It will take [itex]\Delta t=\frac{l}{u}[/itex] more time for the sound wave to reach the rock, and by then the car will have crossed [itex] s = v \cdot t_{2}[/itex]

where [itex]t_{2} = t_{1} + \Delta t[/itex]

But I'm stuck here. How exactly does a sound wave echo? If it just bounces back, it will miss the car of course, so does it perhaps reflect in some radial form? If it does, how should I calculate the point there the sound and the trajectory of the car intersect?

Of course, I think we can assume that [itex]v << u[/itex], otherwise there wouldn't be any point to any of this. Also disregard that the magnitudes of the arrows (like velocity, for instance) are different in the different pictures, I did it to make the pictures more clearer.

Thanks in advance.

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