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# 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 - Physics

#### Question

For the travelling harmonic wave

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

Where and are in cm and 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 1

Equation for a travelling harmonic wave is given as:

y (xt) = 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, = 2 cm

Angular frequency, ω= 20 π rad/s

Phase difference is given by the relation:

phi = kx = 2pi/lambda

(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 = lambda/2

phi = 2phi/lambda xx lambda/2 = pi "rad"

(d) For x = (3lambda)/4

phi = 2pi/lambda xx 3lambda/4 = 1.5 pi rad

#### Solution 2

The given equation can be drawn be rewritten as under

y(x, t) = 2.0 cos [2pi (10t - 0.0080x) + 2pi xx 0.35]

or y(x,t) = 2.0 cos [2pi xx 0.0080((10t)/0.0080 - x)+0.7pi]

Comparing this equation with the standard equation of a travelling harmonic wave.

(2pi)/lambda = 2pi  xx  0.0080  or lambda = 1/0.0080cm = 125 cm

The phase difference between oscillatory motion of two points seperated by a distance trianglex is given by

trianglephi  = (2pi)/lambda trianglex

a) When triangle z = 4 m = 400 cm then

trianglephi = (2pi)/125 xx 400 = 6.4 pi " rad"

b) When triangle x = 0.5 m = 50 cm, then

trianglephi = (2pi)/125 xx 50 = 0.8 pi  "rad"

c) When trianglex  = lambda/2 = 125/2 cm , then

triangle phi  = (2phi)/125 xx 125/2 = pi "rad"

d) When trianglex  =  (3lambda)/4 = (3xx125)/4 cm, then

triangle phi = (2phi)/125 xx (3xx125)/4 = (3pi)/2 "rad"

Is there an error in this question or solution?

#### APPEARS IN

Solution 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 Concept: The Speed of a Travelling Wave.
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