y = Asin (wt+kx) eq of wave or particle?? Related: Waves (Transverse and Longitudinal) - Waves, Class 11, Physics

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y = Asin (wt+kx) eq of wave or particle?? Related: Waves (Transverse ...

y=Asin(ωt−κx)y=Asin(ωt−κx).

It comes from while determining the wave function of a sinusoidal wave.

Suppose a sinusoidal wave travels from left to right (the direction of increasing x) along the string.

Let’s construct its wave function.

Every particle of the string oscillates with simple harmonic motion with the same amplitude and frequency. Suppose that the displacement of a particle at the left end of the string (x=0)(x=0), where the wave originates, is given by y=Asinωty=Asinωt ——→ i.

The wave disturbance travels from x=0x=0 to some point x to the right of the origin in an amount of time given by x/vx/v, where vv is the wave speed. So the motion of point xx at time tt is the same as the motion of point x=0x=0 at the earlier time t−x/vt−x/v. Hence we can find the displacement of point xx at time tt by simply replacing tt by (t−x/v)(t−x/v) in i.

Putting t=(t−x/v)t=(t−x/v) in i,

y=Asinω(t−x/v)y=Asinω(t−x/v)

or, y=Asin(ωt−κx)y=Asin(ωt−κx) ∵ω/v=κ∵ω/v=κ

Similar procedure would follow for wave going in negative direction.

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