Example of waves | Learn Physics

Example of waves

Example  of waves:  A progressive and a stationary simple harmonic wave each has the same frequency of 250 Hz, and the same velocity of 30 m/s. calculate

(i)                  Phase difference between two vibrating points on the progressive wave, which are 10 cm apart.

(ii)                The equation of motion of progressive wave of its amplitude is 0.01 m.

(iii)               The distance between the nodes in the stationary wave,

(iv)              The equation of motion of the stationary wave if its amplitude is 0.03 m.

Solution:     Here,  v = 250 Hz, v= 30 m/s

                       λ = u/v = 30/250 =3/25 m =12 cm

(i)                 Phase difference between two vibration pts separated by λ = 12 cm is 2π

Phase difference between two points 10 cm apart = (2π /12) × 10 = 5π/3 radian

(ii)               The general equation of plane progressive wave is

Y = r sin [(2πt/T)-(2πx/ λ)

Y= 0.01 sin 2π (250t -25x/3)

(iii)              Distance between nodes in a stationary wave =λ/2=12/2=6 cm

(iv)             Equation of stationary wave is given by

Y = 2a cos (2πx/λ) sin(2πvt/λ)

Y= 0.03 cos (5 π x/3) sin 500 πt

Note that here, amplitude 0f stationary wave is 2a = 0.03 m.