# What is the distance between the cliffs?

1. Jan 24, 2005

### Bri

A cowboy stands on horizontal ground between two parallel vertical cliffs. He is not midway between the cliffs. He fires a shot and heras its echoes. The second echo arrives 1.92 s after the first and 1.47 s before the third. Consider only the sound traveling parallel to the ground and reflecting from the cliffs. Take the speed of sound as 340 m/s. What is the distance between the cliffs?

I just can't figure this out, I don't know how to set it up.

2. Jan 25, 2005

### Curious3141

This is a nice problem, more a common sense poser than a physics problem.

Let's call the cliffs 1 and 2, and he's standing closer to cliff 1. The sound of the gunshot will go in opposite directions, hitting cliff 1 and cliff 2. Obviously, it'll reach cliff 1 first. So the first echo is heard when the sound has travelled twice the distance from the gun to cliff 1 to reach the man's ears.

The second echo is heard when the sound has bounced off cliff 2 and come back to him (i.e. distance travelled = twice the distance from man to cliff 2).

The third echo will be heard when the reflected sound that bounced off cliff 2 goes past the man, bounces off cliff 1 and comes back. You can work out the distance that sound has travelled.

You need to solve for the distance between the man and each cliff (then you can add them for the final answer). You're given the time intervals between echos. You know that time = distance/speed. Can you set up the equations and solve them now ?

Last edited: Jan 25, 2005