Question:
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

Answer:

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

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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Question:
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

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Question: 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

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Question:
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