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Grade: upto college level
        A wave propagates on a string in the positive x-direction at a velocity v. The shape of the string at t = t0 is given by g(x, t¬0) = A sin(x/a). Write the wave equation for a general time t. 
5 years ago

Answers : (1)

Aditi Chauhan
askIITians Faculty
396 Points
							Sol. At t = t0, g(x, t0) = A sin (x/a) …(1)
For a wave traveling in the positive x-direction, the general equation is given by
y = f(x/a – t/T)
Putting t = –t0 and comparing with equation (1), we get
⇒ g(x, 0) = A sin {(x/a) + (t0/T)}
⇒ g(x, t) = A sin {(x/a) + (t0/T) – (t/T)}
As T = a/v (a = wave length, v = speed of the wave)
⇒ y = A sin (x/a + t0/(a/v) – t/(a/v))
= A sin (x + v(t0 - t)/a)
⇒ Y = A sin [x – v(t – t0/a)]

						
5 years ago
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