Question:

The equation of a stationary wave is:
y=2asin(2πntλ)cos(2πxλ)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:

Updated On: Nov 26, 2024
  • The dimensions of nt nt is [L][L]
  • The dimensions of n n is [LT1][LT^{-1}]
  • The dimensions of n/λ n / \lambda is [T][T]
  • The dimensions of x x is [L][L]
Hide Solution
collegedunia
Verified By Collegedunia

The Correct Option is C

Solution and Explanation

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

Analyzing the dimensions:
[nλ]=[ω]=[T1] \left[\frac{n}{\lambda}\right] = [\omega] = [T^{-1}]  

For the other terms:
[nt]=[λ]=[L],[n]=[λω]=[LT1],[x]=[λ]=[L] [nt] = [\lambda] = [L], \quad [n] = [\lambda \omega] = [LT^{-1}], \quad [x] = [\lambda] = [L]  

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

Was this answer helpful?
0
0

Top Questions on Waves

View More Questions