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We know the equation of a plain progressive simple harmonic wave going from left to right is, $$y=a\sin\frac{2\pi}{\lambda}(vt−x).$$ If we put $t=0$ and $x=0$, we get $y=0$; and if we put $t=0$ and $x= 0.25 \lambda$, we get $y= a$

But How could this be possible? How could right side particles start oscillation before the left ones? Don′t it need a certain time gap for right side particles to start oscillating?

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  • $\begingroup$ Which wave is this? what is "y"? $\endgroup$
    – Ofek Gillon
    Commented Aug 27, 2021 at 16:57
  • $\begingroup$ Any simple harmonic progressive wave $\endgroup$
    – MD Hossain
    Commented Aug 27, 2021 at 16:58
  • $\begingroup$ Lets say it's an electromagnetic wave. What is the problem exactly? $\endgroup$
    – Ofek Gillon
    Commented Aug 27, 2021 at 17:00
  • $\begingroup$ No i am not talking about EM waves..consider sound wave or waves in a string $\endgroup$
    – MD Hossain
    Commented Aug 27, 2021 at 17:01
  • $\begingroup$ what particles are you talking about? A sine wave is a continuous wave, there is not particles involved in it. And how does $x=0.5\lambda$ give you $y=-a$, $y=\sin \pi = 0$! I don't understand this time gap you are talking about. What exactly are you asking? $\endgroup$
    – TheImperfectCrazy
    Commented Aug 27, 2021 at 17:04

1 Answer 1

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A sinusoidal wave means that a sine wave profile has already established on the string. Probably, you are thinking about the initial stage of building up the wave by an oscillating drive in one end of the string (the transient period.) During the transient period, the wave on the string is not called a sinusoidal wave.

after the period, a sine wave is built on the string. At a fixed time (as $t=0$ of your choice), the profile of the string vertical displacement is a sine wave: $$ y(x, t=0) = a \sin k x. $$ where $k = \frac{2\pi}{\lambda}$ is the wave number.

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  • $\begingroup$ You mean,, this equation don't work when all the particles yet not start oscillating i.e. at the stage of starting the wave? $\endgroup$
    – MD Hossain
    Commented Aug 27, 2021 at 17:42
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    $\begingroup$ Yes. The equation is valid only after the wave is established. $\endgroup$
    – ytlu
    Commented Aug 27, 2021 at 17:45
  • $\begingroup$ ytlu - I thought when t=0 the wave will just start from this moment.What we actually mean by t=0?? $\endgroup$
    – MD Hossain
    Commented Aug 27, 2021 at 17:50
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    $\begingroup$ The equation doesn't tell you when the wave was created. $t=0$ is arbitrarily established once the wave exists. $\endgroup$
    – Bill N
    Commented Aug 27, 2021 at 17:52
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    $\begingroup$ Thank you sir it was my first stack question. $\endgroup$
    – MD Hossain
    Commented Aug 27, 2021 at 19:19

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