Question

Equation of plane progressive transverse wave in a dissipative medium has general form

$y = \text{A}\text{e}^{- \alpha_{x}}\sin\beta(t\ - \ Βx)$ wherea, A, B, C are constant, x & y are displacement & t is time. Dimensions of a, b& B respectively are –

• A. $M^{0}L^{\text{-1}}T^{0}\text{, }\text{M}^{0}L^{\text{-1}}T^{\text{-1}}\text{, }\text{M}^{0}\text{L}\text{T}^{\text{-1}}$
• B. $M^{0}L^{1}T^{0}\text{, }\text{M}^{0}L^{0}\text{ }\text{T}^{\text{-1}}\text{, }\text{M}^{0}L^{\text{-1}}T^{1}$
• C. $M^{0}L^{\text{-1}}T^{1}\text{, }\text{M}^{0}L^{\text{-1}}\text{T, }\text{M}^{0}L^{0}T^{\text{-1}}$
• D. $M^{0}L^{\text{-1}}T^{0}\text{, }\text{M}^{0}L^{0}\text{ }\text{T}^{\text{-1}}\text{, }\text{M}^{0}L^{\text{-1}}T^{1}$

Answer 1

Answer: (D)

$M^{0}L^{\text{-1}}T^{0}\text{, }\text{M}^{0}L^{0}\text{ }\text{T}^{\text{-1}}\text{, }\text{M}^{0}L^{\text{-1}}T^{1}$

Answer 2

By def. [ax] = 1̃ [a] $= \text{ }\text{M}^{0}L^{\text{-1}}T^{0}$

[Bx] = [t] ̃ [B] $= \text{ }\text{M}^{0}L^{\text{-1}}T^{1}$

[bt] = 1̃ [b] $= \text{ }\text{M}^{0}L^{0}T^{\text{-1}}$