Question

Two waves are represented by $y_1=4\sin 404\pi t$ and $y_2=3\sin 400\pi t.$ Then

• A. beat frequency is 4 Hz and the ratio of maximum to minimum intensity is 49 : 1
• B. beat frequency is 2 Hz and the ratio of maximum to minimum intensity is 49 : 1
• C. beat frequency is 2 Hz and the ratio of maximum to minimum intensity is 1 : 49
• D. beat frequency is 4 Hz and the ratio of maximum to minimum intensity is 1 : 49

Answer 1

Answer: (B)

Given, $y_1=4sin404\pi t,y_2=3sin400\pi t$
Comparing with equation y = A sin $\omega t,$
$\therefore {\omega }_1=404\pi ,{\omega }_2=400\pi ,A_1=4,A_2=3$
$\because {\omega }_1=2\pi v_1\Rightarrow 404\pi =2\pi v_1$
or $v_1=202Hz$
${\omega }_2=2\pi v_2$
$\Rightarrow 400\pi =2\pi v_2$
or $v_2=200Hz$
Beat frequency = $v_1-v_2=202-200=2Hz$
$\frac{I_{max}}{I_{min}}=(\frac{A_1+A_2}{A_1-A_2}{)}^2=(\frac{4+3}{4-3}{)}^2$
$=(\frac{7}{1}{)}^2=\frac{49}{1}$