JEE Main · 2021 · 17 Mar 2021 · Shift 2 · Waves & Sound

A sound wave of frequency 245 Hz travels with the speed of

300 ms^{- 1}

along the positive x -axis. Each point of the wave moves to and for through a total distance of 6 cm . What will be the mathematical expression of this traveling wave?

(A) $Y (x, t) = 0.03 [sin 5.1 x - (1.5 \times 1 0^{3}) t]$ ✓ Correct
(B) $Y (x, t) = 0.03 [sin 5.1 x - (0.2 \times 1 0^{3}) t]$
(C) $Y (x, t) = 0.06 [sin 5.1 x - (1.5 \times 1 0^{3}) t]$
(D) $Y (x, t) = 0.06 [sin 0.8 x - (0.5 \times 1 0^{3}) t]$

Answer: (A)

Solution

Each particle of the medium swings between the two extremes of its motion, a span of

2 A

, so

2 A = 6

cm and the amplitude is

A = 0.03

m. The angular frequency and the wave number are

ω = 2 π f = 2 π (245) = 1.5 \times 1 0^{3} rad s^{- 1}

k = \frac{ω}{v} = \frac{1.5 \times 1 0 ^{3}}{300} = 5.1 m^{- 1}

For a wave moving along

+ x

the displacement in metres is

Y (x, t) = 0.03 sin [5.1 x - (1.5 \times 1 0^{3}) t]

JEE Main · 2021 · 17 Mar 2021 · Shift 2 · Single correct option

Practise more: all JEE Main PYQs on Waves & Sound →

JEE Main · 2021 · 17 Mar 2021 · Shift 2 · Waves & Sound

Solution

More JEE Main questions on Waves & Sound