Question

Ina a simple harmonic wave what should be the minimum distance between particles in same phase always having same speed ?

Answer 1

To find:

Minimum distance between particles in a simple harmonic wave having the same phase and same speed.

Calculation:

Let a sine wave be as :

$y = a \sin( \omega t - kx)$

Now , Velocity of particles at any point ;

$v = \dfrac{ \partial(y)}{ \partial t}$

$= > v = \dfrac{ \partial(y)}{ \partial t} = a \omega \cos( \omega t - kx)$

$\boxed{ = > v = \dfrac{ \partial(y)}{ \partial t} =slope}$

Now , refer to the attached diagram;

At a distance of $\lambda$ , the particles of the wave have the same phase with the same slope.

Hence , their velocities are also same.

So, final answer is:

$\boxed{ \sf{minimum \: \: distance = \lambda}}$