Question

If a progressive wave and a stationary wave have frequency 300 Hz and the same
wave velocity 360 m/s, then calculate,
(i) The phase difference between two points on the progressive wave which are 0.4 m
apart.
(ii) The equation of motion of progressive wave if its amplitude is 0.02 m
(iii) The equation of the stationary wave if its amplitude is 0.01 m
(iv) The distance between consecutive nodes in the stationary wave.

Answer 1

Given :

Wave velocity=V=360m/s

Frequency=n=300Hz

Wavelength =λ=V/f

=360/300=1.2m

 i) The phase difference two points at a distance one wavelength apart is 2π

The phase difference two points at a distance 0.4m apart is (2π/λ )x0.4
= (2xΠ/1.2)x 0.4radian
=2Π/3 radian

II) The equation of motion of progressive wave is y= Asin2π(t/T - x/λ)
y=0.02Sin2π(300t -x/1.2)

iii) equation of stationary wave  is y=2Acos 2πx/λ sin 2πt/T

2A=2x0.01=0.02λ=1.2m
1/T=300Hz
y=0.02Cos2πx/1.2 Sin600πt

Iv) The distane between the two consective nodes in staionary wave is given by λ/2= 1.2/2= 0.6m