Q140 / 160 · TS EAMCET 2024 (11 May Shift 1) · Physics

The displacement equations of sound waves produced by two sources are given by $y_1=5 \sin 400 \pi t$ and $y_2=$ $8 \sin 408 \pi t$, where ' $t$ ' is time in seconds. If the waves are produced simultaneously, the number of beats produced per minute is

  • A
    $4$
  • B
    $8$
  • C
    $120$
  • Correct answer
    D
    $240$

Solution

$\begin{aligned} & \quad \mathrm{y}_1=5 \sin 400 \pi \mathrm{t}, \mathrm{y}_2=8 \sin 408 \pi \mathrm{t} \\ & \therefore \quad \omega_1=400 \pi, \omega_2=408 \pi \end{aligned}$ $\therefore \quad$ Number of beats per minute is $\begin{aligned} & 60\left|\mathrm{f}_1-\mathrm{f}_2\right|=60\left|\frac{\omega_1}{2 \pi}-\frac{\omega_2}{2 \pi}\right|=60\left|\frac{400 \pi}{2 \pi}-\frac{408 \pi}{2 \pi}\right| \\ & =240 \text { cycle } / \mathrm{min} \end{aligned}$

Hence, the correct answer is option: 'D'.

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