JEE Main · 2019 · 12 Jan 2019 · Shift 1 · Waves & Sound

A travelling harmonic wave is represented by the equation

y (x, t) = 1 0^{- 3} sin (50 t + 2 x)

, where

x

and

y

are in meter and

t

is in seconds. Which of the following is a correct statement about the wave?

(A)The wave is propagating along the negative $x$ -axis with speed $25 ms^{- 1}$ .✓ Correct
(B)The wave is propagating along the positive $x$ -axis with speed $100 ms^{- 1}$ .
(C)The wave is propagating along the positive $x$ -axis with speed $25 ms^{- 1}$ .
(D)The wave is propagating along the negative $x$ -axis with speed $100 ms^{- 1}$ .

Answer: (A)

Solution

Compare

y = 1 0^{- 3} sin (50 t + 2 x)

with the standard travelling wave

y = A sin (ω t \pm k x)

. The plus sign between the time and space terms means the wave moves in the negative

x

-direction, since the phase

ω t + k x

stays constant only when

x

decreases as

t

increases. Reading off

ω = 50 rad/s

and

k = 2 rad/m

, the speed is

v = \frac{ω}{k} = \frac{50}{2} = 25 m/s

. So the wave travels along the negative

x

-axis at

25 m/s

JEE Main · 2019 · 12 Jan 2019 · Shift 1 · Single correct option