Given that, y=Asin2πλ(ct−x), where y and x are measured in meter. Which of the following statements is true?
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a
The unit of λ is same as that of x and A.
b
The unit of λ is same as that of x but not of A.
c
The unit of c is same as that of 2πλ.
d
The unit of (c t-x) is same as that of 2πλ.
answer is A.
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Detailed Solution
As in y=Asin2πλ(Ct-x)sin2πλ(Ct−x) is dimensionless so dimensions of y and A are sameY = A = [L]…..(i)As Ctλ-Xλ is dimensionless so, Ctλ,Xλ are also dimensionless Hence, dimensions of X and λ are sameX = λ = [L] ….(ii)From (i) and (ii) we can say that dimensions of Y, A, X, λ are same.As Ctλ is dimensionless, dimensions of C must be same as of λt and not same as of 2πλ