Question

A source of sound produces 20 compressions and 20 rarefactions in 0.2 seconds. The distance between a compression and consecutive rarefaction is 50 cm. Find speed of wave?

Answer 1

As Wavelength is the distance between tow consecutive compression or rarefraction.

Wavelength = 50 x 2 = 100 cm = 1 m.

1 compression and 1 rarefaction makes a complete wave. Therefore 20 compressions and 20 rarefactions makes 20 waves in 0.2 sconds.

We know that the frequency of a wave is the number of waves produced in 1 second.

So, frequency = 20/0.2

f = 100 Hz

Frequency = 1/time period

T= 1/f

T = 1/100 = 0.01 sec

Now, $Speed=\frac{Wavelength}{Timeperiod}$

$Speed=\frac{1m}{0.01s}=100m/s$.

Thus, the speed of the wave is 100 m/s.