A) \[\frac{y}{a}\]
B) \[bt\]
C) \[cx\]
D) \[\frac{b}{c}\]
Correct Answer: D
Solution :
Given, \[y=a\,\sin (bt-cx)\] Comparing the given equation with general wave equation \[y=a\,\sin \,\,\left( \frac{2\pi t}{T}-\frac{2\pi x}{\lambda } \right)\] we get \[b=\frac{2\pi }{T},\,c=\frac{2\pi }{\lambda }\] [a] Dimensions of \[\frac{y}{a}=\frac{metre}{metre}=\frac{[L]}{[L]}\] = Dimensionless [b] Dimensions of \[bt=\frac{2\pi }{T},\,t=\frac{[T]}{[T]}\] = Dimensionless [c] Dimensions of \[cx=\frac{2\pi }{\lambda }.x=\frac{[L]}{[L]}\] = Dimensionless [d] Dimensions of \[\frac{b}{c}={\frac{2\pi }{T}}/{\frac{2\pi }{\lambda }}\;\] \[=\lambda /T=[L{{T}^{-1}}]\] Thus, option has dimensions.
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