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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?

2 Answers
Mar 7, 2016


The speed is 342.5 metres per second.


The sound has to travel to the cliff and back again. So the sound travels #2xx685m= 1370m#

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.

#(1370-:4)/(4-:4) = x/1#

#(342.5" metres")/(1" second") = x/1#

So the speed is 342.5 metres per second.

Mar 7, 2016


I found #342.5m/s#


The sound has to travel twice the distance to go and come back to be heard:
Speed is #="distance"/"time"=(2xx685)/4=342.5m/s#