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].