Question

Two simple harmonic waves having the same amplitude and frequency with zero phase difference superimpose at right angles to each other. The resultant motion will be

• A. linear
• B. eliptical
• C. circular
• D. none of these

Answer 1

Answer: (A)

linear

The wave equation for the propagating wave along y direction is given by
$x=A\sin (\omega t+\varphi )$..... (1). (Note that the displacement is along x direction when the wave is propagating in y direction and vice-versa)
The wave equation for the propagating wave along x direction is given by
$y=A\sin (\omega t+\varphi )$...... (2).
From Eq. (1) and Eq. (2), we get $x=y$.
Hence the resultant motion will be linear.