Question

1. For the travelling harmonic wave
y(x, t) = 2 cos2π(10t - 0.008x + 0.35) where x and y are in cm and t is in s. The phase difference between oscillatory motion of two points separated by a distance of 0.5 m is​

Answer 1

Answer:

Equation for a travelling harmonic wave is given as:

y(x,t)=2.0cos2π(10t−0.0080x+0.35)

=2.0cos(20πt−0.016πx+0.70π)

Where,

Propagation constant, k=0.0160π

Amplitude, a=2cm

Angular frequency, ω=20πrad/s

Phase difference is given by the relation:

ϕ=kx=2π/λ

(a) For Δx=4m=400cm

Δϕ=0.016π×400=6.4πrad

(b) For Δx=0.5m=50cm

Δϕ=0.016π×50=0.8πrad

(c) For Δx=λ/2

Δϕ=2π/λ×λ/2=πrad

(d) For Δx=3λ/4

Δϕ=2π/λ×3λ/4=1.5πrad.