15.10 For the travelling harmonic wave y(x, t)=2.0cos2π10t0.0080x+0.35

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

(a) 4 m,

(b) 0.5 m,

(c) λ/2,

(d) 3λ/4


The equation for a travelling harmonic wave is given as:
y(x, t)=2.0cos2π10t0.0080x+0.35=2.0cos20πt0.016πx+0.70π
Propagation constant, k = 0.0160π
Amplitude, a = 2 cm
Angular frequency, ω= 20π rad/s
Phase difference is given by:
ϕ=kx=2πλx
For x = 4 m = 400 cm,
Φ = 0.016 π × 400 = 6.4 π rad
For x = 0.5 m = 50 cm,
Φ = 0.016 π × 50 = 0.8 π rad
For x=λ2,
ϕ=2πλ×λ2=π rad
For x=3λ4,
ϕ=2πλ×3λ4=1.5π rad