Two vibrating tuning forks produce progressive waves given by y_1… - Vidyadip

MCQ

Two vibrating tuning forks produce progressive waves given by $y_1= 4 \sin (500 \, \pi t)$ and $y_2= 2 \sin (506 \, \pi t)$. These tuning forks are held near the ear of a person. The person will hear

A
$3\, beats/s$ with intensity ratio between maxima and minima equal to $4$
✓
$3 \,beats/s$ with intensity ratio between maxima and minima equal to $9.$
C
$6\, beats/s$ with intensity ratio between maxima and minima equal to $4.$
D
$6\, beats/s$ with intensity ratio between maxima and minima equal to $9.$

✓

Answer

Correct option: B.

$3 \,beats/s$ with intensity ratio between maxima and minima equal to $9.$

b
$Y_{1}=4 \sin (500 \pi t), Y_{2}=2 \sin (506 \pi t)$

$\mathrm{n}_{1}=250 \mathrm{\,Hz}, \mathrm{n}_{2}=253 \mathrm{\,Hz}$

No. of Beats $=n_{1}-n_{2}=3$

$\mathrm{I}_{1} \propto 16, \mathrm{I}_{2} \propto 4$

$\frac{I_{\max }}{I_{\min }}=\frac{(\sqrt{I_{1}}+\sqrt{I_{2}})^{2}}{(\sqrt{I_{1}}-\sqrt{I_{2}})^{2}}=\left(\frac{4+2}{4-2}\right)^{2}=\left(\frac{6}{2}\right)^{2}=9$

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