# A hiker shouts towards a vertical cliff 465 m away. The echo is heard 2.75 s later. The wavelength of the sound is 0.750 m. Whats the frequency and period of the wave? Is this correct:...

A hiker shouts towards a vertical cliff 465 m away. The echo is heard 2.75 s later.

The wavelength of the sound is 0.750 m. Whats the frequency and period of the wave?

Is this correct:

F=1/t F=1/2.75s =.364 Hz

T=1/f T= 1/.364 Hz= 2.75 s

Is this to correct sig figs?

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### 1 Answer

The velocity of a sound wave is calculated by multiplying the frequency of the wave by the wavelength.

v = fl where f is the frequency in Hz and l is the wavelength in meters.

In this case, you should first find the velocity of the wave, then use that to find the frequency. From the frequency you can then calculate the period.

So, lets find the velocity of the sound wave.

velocity = distance/time. You know the distance = 465m, and the time it takes to get to the cliff is 1/2 the time it takes for the shout to hit the cliff and return. So the time is 2.75/2 = 1.375 s

therefore the velocity of the wave is 465 m/1.375s = 338.2 m/s

Now use that velocity along with the wavelength given to find the frequency of the sound.

338.2 = .750 m * f

then f = 338.2/.75 = 450.9 Hz

Sinc T = 1/f, then T = 1/450.9= 0.0022s