A travelling harmonic wave is given as: y(x, t)=2.0 \cos 2 \pi(10 t-0.0080 x+0.35). What is the phase difference between the oscillatory motion of two points separated by a distance of:
(i) \boldsymbol{\lambda} / 2,
(ii) 6 \lambda / 4
[ X and y are in \mathbf{c m} and t is in secs ].
A travelling harmonic wave is given as: y(x, t)=2.0 \cos 2 \pi(10 t-0.0080 x+0.35). What is the phase difference between the oscillatory motion of two points separated by a distance of:
(i) \boldsymbol{\lambda} / 2,
(ii) 6 \lambda / 4
[ X and y are in \mathbf{c m} and t is in secs ].

Equation for a travelling harmonic wave is given as,

\begin{array}{l} y(x, t)=2.0 \cos 2 \pi(10 t-0.0080 x+0.35) \\ =2.0 \cos (20 \pi t-0.016 \pi x+0.70 \pi) \end{array}

where,

Propagation constant is \mathrm{k}=0.0160 \mathrm{~m}

Amplitude is \mathrm{a}=2 \mathrm{~cm}

Angular frequency is \omega=20 \mathrm{~m} \mathrm{rad} / \mathrm{s}

Phase difference is represented as \Phi=\mathrm{kx}=2 \pi / \lambda

(i) For x=\lambda / 2
\Phi=(2 \pi / \lambda) \times(6 \lambda / 4)
=3 \mathrm{~m} \mathrm{rad}

(ii) For x=6 \lambda / 4
\phi=(2\pi/\lambda)\times(6\lambda/4)
=3m rad