A wave represented by the equation y= a cos( kx- wt) is superimposed with another wave to form a stationary wave such that point x=0 is a node. The equation for the other wave is? Answer is -a cos( kx + wt) . Pls solve and explain the solution elaborately. Thanks
Dear Student,
Please find below the solution to the asked query:
If two waves are superimposed to create a standing wave then,
y = a (cos kx cos wt - sin kx sin wt)
now,
to eliminate the time component we need to add [-a (cos kx cos wt + sin kx sin wt)] to make the resulting wave a standing wave.
now,
[-a (cos kx cos wt + sin kx sin wt)] is the equation of the wave that needs to be added to get the desired result.
Thus,
y' = -a cos(kx +wt) is the required answer.
Hope this information will clear your doubts about (waves).
If you have any more doubts just ask here on the forum and our experts will try to help you out as soon as possible.
Regards
Satyendra Singh
Please find below the solution to the asked query:
If two waves are superimposed to create a standing wave then,
- both should be travelling in opposite directions.
- they should result into a waveform such that the time dependence of the resulting wave is elemimated.
y = a (cos kx cos wt - sin kx sin wt)
now,
to eliminate the time component we need to add [-a (cos kx cos wt + sin kx sin wt)] to make the resulting wave a standing wave.
now,
[-a (cos kx cos wt + sin kx sin wt)] is the equation of the wave that needs to be added to get the desired result.
Thus,
y' = -a cos(kx +wt) is the required answer.
Hope this information will clear your doubts about (waves).
If you have any more doubts just ask here on the forum and our experts will try to help you out as soon as possible.
Regards
Satyendra Singh