Question

The equation of a progressive wave, where t is the time in second, x is the distance in meter is y = Acos240( t - x/12) . The phase difference (in SI units) between two positions 0.5m apart is ?

Answer 1

The phase difference of both the points is 10 radians.

Explanation :

We have the wave equation as :

y = Acos240( t - x/12)

comparing this with the standard wave equation we get ,

Phase₁ = 240 x/12 = 20x

Now at another point which is at 0.5 meters away , wave equation will be

y = Acos240( t - (x+0.5)/12)

Hence,

phase₂ = 240(x+0.5)/12

= 20(x + 0.5)

= 20x + 10

Hence phase difference of both the points = phase₂ - Phase₁

= 20x + 10 -20x

=10

Hence the phase difference of both the points is 10 radians.