if displacement wave equation of a sound wave is given as s=Asin(Bx-Ct) then dimensions of A^2*C/B is ( s is displacement of particle which is at x=x at any time t)
Answers
Given : if the displacement wave equation of a sound wave is given as s = Asin(Bx - Ct)
To find : The dimensions of A²C/B
solution : dimension of A = dimension of s
= [L]
we know, sine function is a dimensionless quantity.
⇒(Bx - Ct) is a dimensionless quantity.
⇒Bx and Ct are also dimensionless quantities.
so dimension of B × dimension of x = 1
⇒dimension of B = 1/dimension of x = 1/[L]
⇒dimension of B = [L¯¹]
again, dimension of C × dimension of t = 1
⇒dimension of C = 1/dimension of t = 1/[T]
⇒dimension of C = [T¯¹]
dimension of A²C/B = [L]² × [T¯¹]/[L¯¹]
= [L³T¯¹]
Therefore the dimensions of A²C/B = [L³T¯¹]
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