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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) $8 \mathrm{~m}$,(ii) $1 \mathrm{~m}$[ $X$ 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) $8 \mathrm{~m}$,
(ii) $1 \mathrm{~m}$
[ $X$ and $y$ are in $\mathbf{c m}$ and $t$ is in secs $]$.
CBSE | Class 11 | NCERT | Physics | Waves
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) $8 \mathrm{~m}$,
(ii) $1 \mathrm{~m}$
[ $X$ 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 $x=8 \mathrm{~m}=800 \mathrm{~cm}$
$\Phi=0.016 \pi \times 800=12.8 \mathrm{mrad}$

(ii) For $x=1 \mathrm{~m}=100 \mathrm{~cm}$

i

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