### Q.10:- For the travelling harmonic wave

*y *(*x, t*) = 2.0 cos 2π (10*t *– 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

**Answer:-**

Equation for a travelling harmonic wave is given as:

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

= 2.0 cos (20π*t* – 0.016π*x* + 0.70 π)

Where,

Propagation constant, *k* = 0.0160 π

Amplitude, *a *= 2 cm

Angular frequency, *ω*= 20 π rad/s

Phase difference is given by the relation:

*Φ *= *kx* = 2π/λ

(a) For *x* = 4 m = 400 cm

*Φ* = 0.016 π × 400 = 6.4 π rad

(b) For 0.5 m = 50 cm

*Φ* = 0.016 π × 50 = 0.8 π rad

(c) For *x* = λ/2

*Φ *= 2π/λ × λ/2 = π rad

(d) For *x* = 3λ/4

*Φ *= 2π/λ × 3λ/4 = 1.5π rad.