A) \[y=a\cos bx\sin ct\]
B) \[y=a\sin bx\cos ct\]
C) \[y=a\sin \,(bx+ct)\]
D) \[y=a\sin \,(bx+ct)+a\sin \,(bx-ct)\]
Correct Answer: C
Solution :
Two superimposing waves are incident wave \[{{y}_{1}}=a\,\sin \,(\omega \,t-kx)\] and reflected wave\[{{y}_{2}}=a\,\sin \,(\omega \,t+kx)\] Then by principle of superposition \[y={{y}_{1}}+{{y}_{2}}\] \[=a[\sin \,(\omega \,t-kx)+\sin \omega \,t+kx)]\] \[\Rightarrow \] \[y=2a\,\cos \,kx\,\sin \,\omega \,t\] Therefore, option doesnot represent a stationary wave.
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