MHT CET · Physics · Waves and Sound
The equation of a simple harmonic progressive wave is given by \(y=A \sin (100 \pi t-3 x)\). Find the distance between 2 particles having a phase difference of \(\frac{\pi}{3}\).
- A \(\frac{\pi}{9} \mathrm{~m}\)
- B \(\frac{\pi}{18} \mathrm{~m}\)
- C \(\frac{\pi}{6} \mathrm{~m}\)
- D \(\frac{\pi}{3} \mathrm{~m}\)
Answer & Solution
Correct Answer
(A) \(\frac{\pi}{9} \mathrm{~m}\)
Step-by-step Solution
Detailed explanation
Given, \(y=A \sin (100 \pi t-3 x)\)
The general equation,
\(
\begin{aligned}
& & y &=A \sin (\omega t-k x) \\
\therefore & & k &=3
\end{aligned}
\)
and
\(
k=\frac{2 \pi}{\lambda}
\)
or
\(
\begin{array}{l}
\lambda=\frac{2 \pi}{k} \\
\lambda=\frac{2 \pi}{3}
\end{array}
\)
Phase difference, \(\phi=\frac{\pi}{3}\)
\(
\frac{2 \pi}{\lambda} \cdot x=\frac{\pi}{3}
\)
or\(
\begin{array}{l}
x-\frac{\pi}{3} \times \frac{\lambda}{2 \pi} \\
x=\frac{\pi}{3} \times \frac{2 \pi}{3 \times 2 \pi}
\end{array}
\)
Distance, \(x=\frac{\pi}{9} \mathrm{~m}\)
The general equation,
\(
\begin{aligned}
& & y &=A \sin (\omega t-k x) \\
\therefore & & k &=3
\end{aligned}
\)
and
\(
k=\frac{2 \pi}{\lambda}
\)
or
\(
\begin{array}{l}
\lambda=\frac{2 \pi}{k} \\
\lambda=\frac{2 \pi}{3}
\end{array}
\)
Phase difference, \(\phi=\frac{\pi}{3}\)
\(
\frac{2 \pi}{\lambda} \cdot x=\frac{\pi}{3}
\)
or\(
\begin{array}{l}
x-\frac{\pi}{3} \times \frac{\lambda}{2 \pi} \\
x=\frac{\pi}{3} \times \frac{2 \pi}{3 \times 2 \pi}
\end{array}
\)
Distance, \(x=\frac{\pi}{9} \mathrm{~m}\)
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