Show that the particle speed can never be equal to the wave speed in a sine wave if the amplitude is less than wavelength divided by 2π.

Question

Show that the particle speed can never be equal to the wave speed in a sine wave if the amplitude is less than wavelength divided by 2 π .

Philoid · Accepted Answer

Equation of the wave is given by,

Velocity of the wave,

velocity of the particle,

Maximum velocity of the particle,

We have been given that,

Therefore,

Hence, we can conclude,