The distance between two consecutive points with phase difference of 60° in a wave of frequency 500 Hz is 6.0 m. The velocity with which wave is travelling is _____ km s$$^{-1}$$.

The distance between two consecutive points with a phase difference of $$60°$$ in a wave of frequency 500 Hz is 6.0 m. Find the wave velocity.

Relate phase difference to wavelength.

The phase difference between two points separated by distance $$\Delta x$$ is:

$$\Delta \phi = \frac{2\pi}{\lambda} \cdot \Delta x$$

Find the wavelength.

$$\Delta \phi = 60° = \frac{\pi}{3}$$ radians, $$\Delta x = 6.0$$ m:

$$\frac{\pi}{3} = \frac{2\pi}{\lambda} \times 6$$

$$\lambda = \frac{2\pi \times 6}{\pi/3} = 2 \times 6 \times 3 = 36 \text{ m}$$

Calculate velocity.

$$v = f\lambda = 500 \times 36 = 18000 \text{ m/s} = 18 \text{ km s}^{-1}$$

The correct answer is 18 km s$$^{-1}$$.