The equation of a wave travelling on a string stretched along the X-axis is given by
.
(A) Write the dimensions of A, a and T. (B) Find the wave speed. (C) In which direction is the wave travelling? (D) Where is the maximum of the pulse located at t = T? At t = 2 T?
A. L, L, T
Exponents are always dimension less. So,
[a]=[L]
[T]=[T]
Exponentials are also dimensionless. But, y is displacement and to sustain that A must have dimension of displacement too. So,
[A]=[L]
B. a/T
Here λ=a
So the speed will be
C. negative x-directions
The whole structure depends upon the exponent.
As,
So, the wave will propagate is the –ve x direction.
D.
x = − a and x = − 2 a
Given equation is
At t = T, Y = A
Similarly, at t=2T, Y=A
1