Question

derivation for displacement equation y = A sin(wt - kx) of a plane progressive wave

Answer 1

Answer:

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Answer 2

Explanation:

Let's take the argument of the function i.e, kx−ωt. The argument of the function should remain constant,(equivalently the phase must remain constant)for a particular section of the wave.

kx−ωt=λ

where λ is a constant. Differentiating both sides we get,

kdxdt=ω

which is positive, thus this represents a wave travelling in positive direction. Similarly for the wave travelling in negative direction.

This can be illustrated by plotting also, the blue wave represents wave at t=0 and the orange wave represents wave at a later time, As you can see, the wave has moved in left direction for the first figure for the equation y=asin(kx+ωt) and in the right for the second i.e for y=asin(kx−ωt) case.Consider the blue wave below at some x, now if you want to make the wave move, then you need the same y at some other x and t, thus for the first case,it happens when x becomes less positive, or moves to the left, implying that the wave has traveled in negative direction.wave travelling in the negative directionwave travelling in the positive direction