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Q.

The equation of the stationary wave is y=2Asin⁡2πctλcos⁡2πxλ Which of the following statements is wrong?

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a

The unit of ct is same as that of λ.

b

The unit of x is same as that of λ.

c

The unit of 2πc/λ is same as that of 2πx/λt.

d

The unit of c/λ is same as that of x/λ.

answer is D.

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Detailed Solution

Here (2πct/λ) as well as (2πx/λ) arc dimensionless. So unit of ct is same as that of λ. Unit of x is same as that of λ. Also,2πctλ=2πxλ=M0L0T0Hence, 2πcλ=2πxλt,, option (d),x/λ is unitless. This is not the case with c/λ.
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