Question
For the travelling harmonic wave,
y (x, t) = 2.0 cos 2π (10t – 0.0080x + 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
Solution
Equation for a travelling harmonic wave is given as:
y (x, t) = 2.0 cos 2π (10t – 0.0080x + 0.35)
= 2.0 cos (20πt – 0.016πx + 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 =
(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.
y (x, t) = 2.0 cos 2π (10t – 0.0080x + 0.35)
= 2.0 cos (20πt – 0.016πx + 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 =
(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.
