Question

Two vibrating tuning forks produce waves given by $y_1=4\sin 500\pi t,$ $y_1=2\sin 506\pi t$ If they are held near the ear of a person, the person will hear

• A. 3 beats/second with intensity ratio of maxima to minima equal to 9
• B. 3 beats/second with intensity ratio of maxima to minima equal to 2
• C. 6 beats/second with intensity ratio of maxima to minima to equal to 2
• D. 6 beats/second with intensity ratio of maxima to minima equal to 9

Answer 1

Answer: (A)

Comparing given equation with standard equations
$y=A\sin \omega t$
We get $A_1=4,{\omega }_1=500\pi$
and $A_2=2,{\omega }_2=506\pi$
Frequency $n=\frac{\omega }{2\pi }$
$\therefore n_1=\frac{{\omega }_1}{2\pi }=\frac{500\pi }{2\pi }=250$
$n_2=\frac{{\omega }_2}{2\pi }=\frac{506\pi }{2\pi }=253$
$\therefore$ number of beats
$=n_2-n_1=253-250=3$
$\frac{I_{\max }}{I_{\min }}=\frac{{\left(A_1+A_2\right)}^2}{{\left(A_1-A_2\right)}^2}$
$=\frac{(4+2{)}^2}{(4-2{)}^2}={\left(\frac{6}{2}\right)}^2=\frac{9}{1}$