Question

The displacement of a travelling wave \( y = C \sin \left( \frac{2\pi}{\lambda} (at - x) \right) \), where \( t \) is time, \( x \) is distance and \( \lambda \) is the wavelength, all in S.I. units. Then the frequency of

• A. \( \frac{2\pi \lambda}{a}\)
• B. \( \frac{2\pi a}{\lambda}\)
• C. \( \frac{\lambda}{a}\)
• D. \( \frac{a}{\lambda}\)

Answer 1

The Correct Option is D

The standard equation for a traveling wave is:

y = A sin(<i>kx</i> − ωt)

Here:

A represents the amplitude.

k denotes the wave number ($k = \frac{2\pi}{\lambda}$).

ω signifies the angular frequency ($\omega = 2\pi f$).

f is the frequency.

Matching this to the provided equation: y = C sin($\frac{2\pi}{\lambda}$(<i>at</i> − x)), we find ω = $\frac{2\pi a}{\lambda}$.

Given that ω = 2πf: 2πf = $\frac{2\pi a}{\lambda}$

$f = \frac{a}{\lambda}$