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) 3 λ/4

Answer 1

Y = 2cos2π(10t - 0.008x + 0.35)
= 2cos(20πt - 0.016πx + 0.7π)
Compare with
Y = acos(wt - Kx + ∅)
w = 20π
K = 0.016π
a = 2 cm
∅ = 0.7π

We know,
∆∅ = 2π/lemda × ∆x
= K.∆x

(a) for ∆x = 4 m = 400 cm
Phase difference (∆∅) = K × 400
∆∅ = 0.016π × 400
= 6.4 rad

(b) for ∆x = 0.5 m = 50 cm
Similarly ,
∆∅ = 0.016π × 50
= 0.8π rad

(c) ∆x = lemda/2

∆∅ = 2π/lemda × lemda/2
= π rad

(d) for ∆x = 3lemda/4
∆∅ = 2π/lemda × 3lemda/4
= 3π/2 rad

Answer 2

$\huge\boxed{\underline{\mathcal{\red{A}\green{N}\pink{S}\orange{W}\blue{E}\purple{R}}}}$.

❤..${6.4\pi rad}$

❤..${0.8 rad}$

❤..${\pi rad}$

❤..${(\pi/2)rad}$