Easy MCQ +4 / -1 PYQ · JEE Mains 2021

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 from through a total distance of 6 cm. What will be the mathematical expression of this travelling wave?

  1. A Y(x, t) = 0.03 [ sin 5.1x $-$ (0.2 $\times$ 10<sup>3</sup>)t ]
  2. B Y(x, t) = 0.03 [ sin 5.1x $-$ (1.5 $\times$ 10<sup>3</sup>)t ] Correct answer
  3. C Y(x, t) = 0.06 [ sin 5.1x $-$ (1.5 $\times$ 10<sup>3</sup>)t ]
  4. D Y(x, t) = 0.06 [ sin 0.8x $-$ (0.5 $\times$ 10<sup>3</sup>)t ]

Solution

$Y = A\sin (kx - \omega t)$<br><br>$A = {6 \over 2}$ = 3cm = 0.03 m<br><br>$\omega = 2\pi f = 2\pi \times 245$<br><br>$\omega = 1.5 \times {10^3}$<br><br>$k = {\omega \over v} = {{1.5 \times {{10}^3}} \over {300}}$<br><br>$k = 5.1$<br><br>$y = 0.03\sin (5.1x - (1.5 \times {10^3})t)$

About this question

Subject: Physics · Chapter: Waves · Topic: Wave Motion and Types

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