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Question

The equation of the stationary wave is
y=2Asin(2πctλ)cos(2πxλ)
Which of the following statements is wrong?

A
The unit of ct is same as that of λ
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B
The unit of x is same as that of λ
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C
The unit of 2πcλ is same as that of 2πxλt
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D
The unit of cλ is same as that of xλ
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Solution

The correct option is D The unit of cλ is same as that of xλ
Here, (2πctλ) as well as (2πxλ) are dimensionless. So, unit of ct is same as that of λ. Unit of x is same as that of λ. Also, [2πctλ]=[2πxλ]=M0L0T0
Hence, [2πcλ]=[2πxλt].
In the option (d), xλ is unitless. This is not the case with cλ.

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