The equation of 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:

The equation is: $$y = 2a\sin\left(\frac{2\pi nt}{\lambda}\right)\cos\left(\frac{2\pi x}{\lambda}\right)$$

For the equation to be dimensionally consistent:

- $$\frac{2\pi x}{\lambda}$$ must be dimensionless, so $$[\lambda] = [L]$$ and $$[x] = [L]$$

- $$\frac{2\pi nt}{\lambda}$$ must be dimensionless, so $$[nt/\lambda]$$ is dimensionless

- This gives $$[n] = [\lambda/t] = [L/T] = [LT^{-1}]$$ (velocity dimension)

Now checking each option:

Option 1: Dimensions of $$n/\lambda = [LT^{-1}]/[L] = [T^{-1}]$$, NOT $$[T]$$. This is NOT correct. ✓ (This is the wrong statement)

Option 2: Dimensions of n is $$[LT^{-1}]$$. Correct.

Option 3: Dimensions of x is [L]. Correct.

Option 4: Dimensions of nt = $$[LT^{-1}][T] = [L]$$. Correct.

The correct answer is Option 1: The dimensions of $$n/\lambda$$ is [T] (this is NOT correct since it should be $$[T^{-1}]$$).