The displacement of a progressive wave is rep | vedclass

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Question

Now, $[\mathrm{LHS}]=[\mathrm{RHS}]$

$[y]=[\mathrm{A}]=\mathrm{L}$

because $\omega t-k x$ is dimensionless,

$[k x]=\mathrm{M}^{0} \mathrm{~L}

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Vedclass · Answer

Now, $[\mathrm{LHS}]=[\mathrm{RHS}]$

$[y]=[\mathrm{A}]=\mathrm{L}$

because $\omega t-k x$ is dimensionless,

$[k x]=\mathrm{M}^{0} \mathrm{~L}^{0} \mathrm{~T}^{0}	herefore[\omega t]=\mathrm{M}^{0} \mathrm{~L}^{0} \mathrm{~T}^{0}$

$	herefore [k] \mathrm{L}=\mathrm{M}^{0} \mathrm{~L}^{0} \mathrm{~T}^{0}$

$	herefore[\omega] \mathrm{T}=\mathrm{M}^{0} \mathrm{~L}^{0} \mathrm{~T}^{0}$

$	herefore [k]=\mathrm{L}^{-1}	herefore[\omega]=\mathrm{T}^{-1}$

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

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