The equation of the stationary wave is $$y=2Asin$$⁡$$2$$$$π$$ctλ$$cos$$⁡$$2$$$$π$$xλ Which of the following statements is wrong?

Correct option is 4The unit of c/λ is same as that of x/λ.

Questions

The equation of the stationary wave is $y = 2 Asin (\frac{2 πct}{λ}) \cos (\frac{2 πx}{λ})$ Which of the following statements is wrong?

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The unit of ct is same as that of λ.

The unit of x is same as that of λ.

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

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

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detailed solution

Correct option is D

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

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The equation of the stationary wave is $y = 2 Asin (\frac{2 πct}{λ}) \cos (\frac{2 πx}{λ})$ Which of the following statements is wrong?