Question

Hi ,

if wave equation Y = a/b+4x² at t= 0
and Y = a/b+ (2x+160)² at t = 2s

Find the direction of propagation and the velocity of wave .

​

Answer 1

Answer:

40m/s towards -ve x-axis.

Explanation:

Substituting $x = -80 + X$ in the equation at t = 2s yields the same form of the equation as that at t = 0, so the wave has travelled from x = 0 to x = -80 in 2 seconds.

This implies that the wave is travelling towards the negative x-axis (-x) and its velocity is: 80/2 unit/s = 40 unit/s.

If x is in m, 40 m/s.

Answer 2

Solution :-

direction ------> - ve (-x)

°•° y = a/b+(kx+ wt)²
y = a/b+ (2x+160)²

at t = 2 sec

•°• y = a/b+ (kx+2w)²

kx= 2x

k = 2

2w = 160

w = 80

v = w/k = 80/2 = 40 m/s Answer ✔