The diagram below shows (a) displacement-time, and (b) displacement-distance, graph of a wave travelling in a string with velocity 20 m `s^(-1)`. In each case, use the graph to calculate the frequency and wavelength of the wave.

Explanation

Given : Wave velocity V = 20 `m s^(-1)`
(a) From graph in Fig. the time for one vibration of particle giving rise to one wave i.e. time period of wave is T = 0.10 s
: Frequency `f=(1)/(T ) = (1)/(0.10 s ) =10 Hz`
From relation V = `f` a,
Wavelength ` lamda = (v)/( f ) = ( 20 ) /(10) = 2m`
(b) From graph in Fig. length of one wave i.e., wavelength `lamda ` = 2 m
From relation `V = f lamda ` ,
Frequency `f= (v)/(lamda) = (20)/(2) = 10 Hz`