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The displacement of a progressive wave i...

The displacement of a progressive wave is represented by `y= A sin (omegat-kx)` where x is distance and t is time. Write the dimensional formula of (i) w and (ii) k.

Text Solution

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Now [LHS]= [RHS]
`[y]=[A]=L`
because `omegat- kx` is dimensionless,
`[kx]=M^(0)L^(0)T^(0) " " :. [omega t]=M^(0)L^(0)T^(0)`
`:. [K]L=M^(0)L^(0)T^(0) " " :. [omega]T=M^(0)L^(0)T^(0)`
`:. [k]=L^(-1) " " :. [omega]=T^(-)`
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