Question

Sounds travels about 750 miles per hour. If you stand in a canyon and sound a horn, you will hear an echoSuppose it takes about 3 second to hear the echo. How far away is the canyon wall, in feet Now let’s generalize that result. Suppose it takes n seconds to hear echo. How far away is the canyon wall in terms of n?

Answer 1

The time it takes to hear an echo can be gotten from the equation;

`t=(2D)/(v)`

Where D is the distance to the wall, v is the speed of sound which is 750 miles per hour.

If it takes 3 seconds to hear an echo, the distance can be gotten by rewriting the equation as;

`D=(vt)/(2)`

Therefore, we find out that;

`D=(750*3)/(2)=1125\text{miles.}`

Therefore, the wall is 1125 miles away.

b. To generalize the result;

If it takes n seconds to hear an echo, the distance to the canyon wall is;

`D=(750n)/(2)=375n`

Therefore, D = 375n