Question

The same progressive wave is represented by two graphs I and II. Graph I shows how the displacement 'y' varies with the distance x along the wave at a given time. Graph II shows how y varies with time t at a given point on the wave. The ratio of measurements AB to CD marked on the curves represents

• A. wave number k
• B. wave speed V
• C. frequency $\nu$
• D. angular frequency $\omega$

Answer 1

The correct option is B wave speed V

In graph $I$, $y$ varies with $x$.

This shows how much the wave travel, $ox$ what is the wave number of the wave.

Thus AB represents the wavelength of the wave.

In graph $II$, $y$ varies with time, $\left(t\right)$

This shows the frequency of the wave with time.

Thus CD represents the time period of the oscillation.

Since,

wave speed$=\frac{\omega }{k}=\frac{2\pi /T}{2\pi /\lambda }[v=\frac{\lambda }{T}]$

$\lambda \to AB,T\to CD$

Hence ratio of measurements AB to CD on the curve represents wave speed.

$\therefore$ option (B) is correct.