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1.Units, Dimensions and Measurement
hard
The equation of stationary wave is
$\mathrm{y}=2 \mathrm{a} \sin \left(\frac{2 \pi \mathrm{nt}}{\lambda}\right) \cos \left(\frac{2 \pi \mathrm{x}}{\lambda}\right)$
Which of the following is NOT correct
A
The dimensions of nt is $[L]$
B
The dimensions of $n$ is $\left[\mathrm{LT}^{-1}\right]$
C
The dimensions of $n / \lambda$ is $[T]$
D
The dimensions of $x$ is $[L]$
(JEE MAIN-2024)
Solution
Comparing the given equation with standard equation of standing $\frac{2 \pi \mathrm{n}}{\lambda}=\omega \& \frac{2 \pi}{\lambda}=\mathrm{k}$
${\left[\frac{\mathrm{n}}{\lambda}\right]=[\omega]=\mathrm{T}^{-1}}$
${[\mathrm{nt}]=[\lambda]=\mathrm{L}}$
${[\mathrm{n}]=[\lambda \omega]=\mathrm{LT}^{-1}}$
${[\mathrm{x}]=[\lambda]=\mathrm{L}}$
Hence option $(3)$
Standard 11
Physics
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