# A hiker shouts toward a vertical cliff 685 m away. The echo is heard 4.00 s later. What is the speed of sound in air?

## The wavelength of the sound is 0.750 m. What is its frequency? What is the period of the wave?

Mar 7, 2016

The speed is 342.5 metres per second.

#### Explanation:

The sound has to travel to the cliff and back again. So the sound travels $2 \times 685 m = 1370 m$

This takes 4.00 seconds

So applying the concept of ratio

Let $x$ be distance in metres

By ratio:" "(1370" metres")/(4.00" seconds")= x/(1" second")

Thus we need to find a way to convert 4 into 1 so that the left side of the = is the same as the right side.

To maintain the ratio of a fraction : what yo do to the top of a fraction you also do to the bottom.

$\frac{1370 \div 4}{4 \div 4} = \frac{x}{1}$

$\left(342.5 \text{ metres")/(1" second}\right) = \frac{x}{1}$

So the speed is 342.5 metres per second.

Mar 7, 2016

I found $342.5 \frac{m}{s}$
Speed is $= \text{distance"/"time} = \frac{2 \times 685}{4} = 342.5 \frac{m}{s}$