JEE Main · 2023 · 25 Jan 2023 · Shift 1 · Waves & Sound

The distance between two consecutive points with phase difference of

6 0^{\circ}

in a wave of frequency 500 Hz is 6.0 m. The velocity with which wave is traveling is ______ km/s

Answer: 18

Solution

Two points a distance

Δ x

apart differ in phase by

Δ ϕ = \frac{2 π}{λ} Δ x

. A phase gap of

6 0^{\circ} = \frac{π}{3}

over

6 m

gives

\frac{π}{3} = \frac{2 π}{λ} \times 6

, so

λ = 36 m

. The wave speed is

v = f λ = 500 \times 36 = 18000 m s^{- 1}

, that is

18 km s^{- 1}

JEE Main · 2023 · 25 Jan 2023 · Shift 1 · Integer answer