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A string of length \( L \) is stretched along \( x \)-axis is rigidly clamped as it ends, it undergoes transverse vibration. If \( n \) is an integer, which of the following relations may represent the shape of the string at any time \( t \) ?
(A) \( y=y_{m} \sin \left(\frac{n \pi x}{L}\right) \cos \omega t \)
(B) \( y=y_{m} \sin \left(\frac{n \pi x}{L}\right) \sin \omega t \)
(C) \( y=y_{m} \cos \left(\frac{n \pi x}{L}\right) \cos \omega t \)
(D) \( y=y_{m} \cos \left(\frac{n \pi x}{L}\right) \sin \omega t \)
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