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.

Question

Philoid · Accepted Answer

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,

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.