Directions : In the following question more than one of the answers given may be correct. Select the correct answer and mark it according to the code:
A transverse sinusoidal wave of amplitude a, wavelength\[\lambda \]and frequency v is travelling on a streched string. The maximum speed of any point on the string is v/10, where v is the speed of the propagation of the wave. If \[a={{10}^{-3}}m\]and\[v=10\text{ }m{{s}^{-1}},\]then\[\lambda \]and v are given by (1) \[\lambda =2\pi \times {{10}^{-2}}m\] (2) \[\lambda ={{10}^{-3}}m\] (3) \[v=\frac{{{10}^{3}}}{2\pi }Hz\] (4) \[v={{10}^{4}}Hz\]A) 1, 2 and 3 are correct.
B) 1 and 2 are correct.
C) 2 and 4 are correct.
D) 1 and 3 are correct.
Correct Answer: D
Solution :
\[{{v}_{\max }}=a\omega =\frac{v}{10}=\frac{10}{10}=1\,m/s\] \[\Rightarrow \] \[q\omega =a\times 2\pi v=1\] \[\Rightarrow \] \[v=\frac{{{10}^{3}}}{2\pi }\] \[(\because a={{10}^{-3}}m)\] Since, \[v=\lambda v\] \[\Rightarrow \] \[\lambda =\frac{v}{v}=\frac{10}{{{10}^{3}}/2\pi }=2\pi \times {{10}^{-2}}m\]
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