Question 330: Waves

Question

A stationery wave is represented by $y=12 \cos \left(\frac{\pi}{6} x\right) \sin (8 \pi t)$, where $x \& y$ are in cm and $t$ in second. The distance between two successive antinodes is

Accepted Answer

To determine the distance between two successive antinodes in a stationary wave, consider the given wave equation:
$ y = 12 \cos \left(\frac{\pi}{6} xight) \sin (8 \pi t) $
This can be compared to the standard form of a stationary wave equation:
$ y = 2A \sin \left(\frac{2 \pi x}{\lambda}ight) \cos \left(\frac{2 \pi t}{\lambda}ight) $
From the comparison, we identify:
$ \frac{\pi}{6} = \frac{2 \pi}{\lambda} $
Solving for $\lambda$:
$ \lambda = 12 \, 	ext{cm} $
The distance between two successive antinodes is given by $\frac{\lambda}{2}$. Therefore, this distance is:
$ \frac{\lambda}{2} = \frac{12\, 	ext{cm}}{2} = 6 \, 	ext{cm} $

Answer

12 cm

Answer

10 cm

Answer

6 cm

Answer

2 cm

Waves

A stationery wave is represented by y=12 \cos \left(\frac{\pi}{6} x\right) \sin (8 \pi t), where x \& y are in cm and t in second. The distance between two successive antinodes is

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