A wave pulse is travelling on a string with a speed υ toward the position 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 equation of the wave for a general time t, if the wave speed is υ.
A. L, L
G(x) is the measure of the height of the ripple. As, sine doesn’t have any dimension; A must have dimension of length.
[A]=[L]
To give a proper value we need to input dimensionless quantities to sine wave. So,
[a]=[L]
B.
Given that wave velocity is v. So, the time period will be,
Here, . So,
Hence,