For the harmonic travelling

Question:

For the harmonic travelling wave y = 2 cos 2 π(10t-0.0080x+3.5) where x and y are in cm and t is second. What is the phase difference between the oscillatory motion at two points separated by a distance of

(a) 4 m

(b) 0.5 m

(c) λ/2

(d) 3 λ/4

(e) what is the phase difference between the oscillation of a particle located at x = 100 cm at t = Ts and t = 5s?

Solution:

Given,

y = 2 cos 2 π(10t-0.0080x+3.5)

a = 2

ω = 20 π

k = 0.016 π

φ = 7 π

(a) path difference, p = 4m = 400 cm

Substituting the values, we get phase difference = 6.4 πrad

(b) path difference, p = 0.5 m = 50 cm

Substituting the values, we get phase difference = 0.8 π rad

(c) path difference, p = λ/2

Substituting the values, we get phase difference = π rad

(d) path difference, p = 3 λ/4

Substituting the values, we get phase difference = 98 π rad

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