MHT CET · Physics · Waves and Sound
A stationery wave is represented by \(y=12 \cos \left(\frac{\pi}{6} x\right) \sin (8 \pi t)\), where \(x \& y\) are in \(c m\) and \(t\) in second. The distance between two successive antinodes is
- A 12 cm
- B 10 cm
- C 6 cm
- D 2 cm
Answer & Solution
Correct Answer
(C) 6 cm
Step-by-step Solution
Detailed explanation
Given equation for stationary wave,
\(y=12 \cos \left(\frac{\pi}{6} x\right) \sin (8 \pi t)\)
Comparing this equation with standard stationary wave equation,
\(y=2 A \sin \left(\frac{2 \pi x}{\lambda}\right) \cdot \cos \left(\frac{2 \pi}{\lambda} t\right)\)
\(\begin{aligned}
& \text { We get, } \\
& \frac{2 \pi}{\lambda}=\frac{\pi}{6} \\
& \therefore \quad \lambda=12 \mathrm{~cm}
\end{aligned}\)
\(\therefore \quad\) Distance between two successive antinodes
\(=\frac{\lambda}{2}=6 \mathrm{~cm}\)
\(y=12 \cos \left(\frac{\pi}{6} x\right) \sin (8 \pi t)\)
Comparing this equation with standard stationary wave equation,
\(y=2 A \sin \left(\frac{2 \pi x}{\lambda}\right) \cdot \cos \left(\frac{2 \pi}{\lambda} t\right)\)
\(\begin{aligned}
& \text { We get, } \\
& \frac{2 \pi}{\lambda}=\frac{\pi}{6} \\
& \therefore \quad \lambda=12 \mathrm{~cm}
\end{aligned}\)
\(\therefore \quad\) Distance between two successive antinodes
\(=\frac{\lambda}{2}=6 \mathrm{~cm}\)
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