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Q.

Given that, y=Asin⁡2πλ(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)sin⁡2πλ(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
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