Class 11 Physics - Chapter Waves NCERT Solutions | For the travelling harmonic wave y (x
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
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:
ø = kx = 2 π / 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 = 2 π / λ x λ / 2 = λ rad
(d) For x = 3λ / 4
Φ = 2 π / λ x 3λ / 4 = 1.5π rad
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