A wave of frequency 500 Hz has wave velocity of 350 m/s. 1)Find the distance between the two points which has #60^o# out of phase. 2)Find the phase difference between two displacements at certain point of time #10^-3#s apart?

1 Answer
Jun 1, 2017

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Given velocity of the wave #v=350m"/"s#

frequency of the wave #n=500Hz#

So wave length of the wave # lambda=v/n=350/500m=0.7m#

1) We are to find the distance between the two points which has #60^@# out of phase i.e the phase difference is #phi=60^@=pi/3 rad#

As we know that for path difference #lambda # there is phase difference #2pi#,

we can say , if #phi # is the phase difference for path difference #x#,then

#phi =(2pix)/lambda#

#x =(philambda)/(2pi)=pi/3xx0.7/(2pi)=0.7/6m~~0.116m#

2) Now in #t=10^-3 s # the wave moves

#vxxt=350xx10^-3=0.35m#

So here path difference #x=0.35m#

So by the relation #phi =(2pix)/lambda#, the phase difference for #x=0.35m# becomes
#phi =(2pixx 0.35)/0.7=pi#,