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 string of length L is stretched along the\[x-\]axis and is rigidly clamped at its two ends. It undergoes transverse vibrations. If n is an integer, which of the following relations may represent the shape of the string at any time t? (1) \[y=A\sin \left( \frac{n\pi x}{L} \right)\cos \omega t\] (2) \[y=A\sin \left( \frac{n\pi x}{L} \right)\sin \omega t\] (3) \[y=A\cos \left( \frac{n\pi x}{L} \right)\cos \omega t\] (4) \[y=A\cos \left( \frac{n\pi x}{L} \right)\sin \omega t\]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: B
Solution :
As the string is rigidly clamped at its two ends therefore,\[y=0\]at\[x=0\]. This can be satisfied only by term\[\sin \frac{n\pi x}{L},\]where n is an integer. Hence, option is correct.
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