For the travelling harmonic wave

y(x, t) = 2.0 cos 2π (10t – 0.0080 x + 0.35)

Where x and y are in cm and t in s. Calculate the phase difference between oscillatory motion of two points separated by a distance of

(a) 4 m,

(b) 0.5 m,

(c) λ/2,

(d) 3λ/4

Given:

Equation of a travelling wave is given by

y(x, t) = 2.0 cos 2π (10t – 0.0080 x + 0.35)

which can be written as,

y(x, t) = 2.0 cos(20 πt – 0.016πx + 0.7 π )

Where,

Propagation constant, k = 0.016 π

Amplitude, a = 2 cm

Angular frequency, w = 20 π rad s^-1

Phase difference is given by the relation,

Φ = kx = 2 π/λ …(1)

a) For x = 4m = 400 cm

Φ = 0.016 π× 400cm = 6.4 π rad

b) For x = 0.5m = 50 cm

Φ = 0.016 π× 50cm = 0.8 π rad

c) For x = λ/2

Φ = 2 π/λ × λ/2 = π rad

d) For x = 3λ/4

Φ = 2 π/λ × 3λ/4 = 3π/2 rad