Question

The equation of a stationary wave is:
$$y = 2a \sin\left(\frac{2\pi nt}{\lambda}\right) \cos\left(\frac{2\pi x}{\lambda}\right)$$Which of the following is NOT correct:

• A. The dimensions of $nt$ is $[L]$
• B. The dimensions of $n$ is $[LT^{-1}]$
• C. The dimensions of $n / \lambda$ is $[T]$
• D. The dimensions of $x$ is $[L]$

Answer 1

The Correct Option is C

Comparing the given equation with the standard equation for a standing wave:
$$\frac{2\pi nt}{\lambda} = \omega t, \quad \frac{2\pi x}{\lambda} = kx$$
where $\omega$ is the angular frequency and $k$ is the wave number.

Analyzing the dimensions:
$$\left[\frac{n}{\lambda}\right] = [\omega] = [T^{-1}]$$ 

For the other terms:
$$[nt] = [\lambda] = [L], \quad [n] = [\lambda \omega] = [LT^{-1}], \quad [x] = [\lambda] = [L]$$ 

Conclusion:
Hence, the dimensions of $n / \lambda$ are [T].