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A wave pulse is travelling on a string with a speed v towards the positive X-axis. The shape of the string at t = 0 is given by g(x) = A sin(x/a), where A and a are constants. (a) What are the dimensions of A and a? (b) Write the equations of the wave for a general time t, if the wave speed is v.
Sol. At t = 0, g(x) = A sin (x/a) a) [M0L1T0] = [L] a = [M0L1T0] = [L] b) Wave speed = v ∴ Time period, T = a/v (a = wave length = λ) ∴ General equation of wave y = A sin {(x/a) – t/(a/v)} = A sin {(x – vt) / a}
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