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A standing wave in a pipe with a length $L=1.2 \mathrm{~m}$ is described by
$y(x, t)=y_{0} \sin [(2 \pi / L) x] \sin [(2 \pi / \mathrm{L}) x+\pi / 4]$
Based on above information, which one of the following statements is incorrect. (Speed of sound in air is $300 \mathrm{~m} \mathrm{~s}^{-1}$ )-
Options:
$y(x, t)=y_{0} \sin [(2 \pi / L) x] \sin [(2 \pi / \mathrm{L}) x+\pi / 4]$
Based on above information, which one of the following statements is incorrect. (Speed of sound in air is $300 \mathrm{~m} \mathrm{~s}^{-1}$ )-
Solution:
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Verified Answer
The correct answer is:
The frequency of the fundamental mode of vibrations is $137.5 \mathrm{~Hz}$
$\begin{array}{l}
\frac{2 \pi}{\lambda} \mathrm{x}=\frac{2 \pi}{\mathrm{L}} \mathrm{x} \\
\therefore \lambda=\mathrm{L}=1.2 \mathrm{~m} \\
\text { at } \mathrm{x}=0, \mathrm{x}=\mathrm{L}, \mathrm{y}=0 \\
\mathrm{v}=\frac{\mathrm{v}}{\lambda}=\frac{300}{1.2}=250 \mathrm{~Hz}
\end{array}$
\frac{2 \pi}{\lambda} \mathrm{x}=\frac{2 \pi}{\mathrm{L}} \mathrm{x} \\
\therefore \lambda=\mathrm{L}=1.2 \mathrm{~m} \\
\text { at } \mathrm{x}=0, \mathrm{x}=\mathrm{L}, \mathrm{y}=0 \\
\mathrm{v}=\frac{\mathrm{v}}{\lambda}=\frac{300}{1.2}=250 \mathrm{~Hz}
\end{array}$
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