Question

Equations of waves produced by two sound sources are $y_1=4\sin 400$$\pi t$ and $y_2=3\sin 404\pi t$.
If an observer is sitting near the sources then he will hear :

• A. $4beats/s$ and $\frac{I_{max}}{I_{min}}=\frac{7}{1}$
• B. $4beats/s$ and $\frac{I_{max}}{I_{min}}=\frac{4}{3}$
• C. $2beats/s$ and $\frac{I_{max}}{I_{min}}=\frac{49}{1}$
• D. $2beats/s$ and $\frac{I_{max}}{I_{min}}=\frac{4}{3}$

Answer 1

Answer: (C)

$2beats/s$ and $\frac{I_{max}}{I_{min}}=\frac{49}{1}$

$y_1=4sin400\pi t\Rightarrow w_1=400\pi =2\pi {\delta }_1\Rightarrow$ ${\delta }_1=200Hz$
$y_2=3sin404\pi t\Rightarrow w_2=404\pi =2\pi {\delta }_2\Rightarrow$ ${\delta }_2=202Hz$
$Beats={\delta }_2-{\delta }_1$
$=202-200$
$=2beats/s$

$\frac{I_{max}}{I_{min}}=\frac{(A_1+A_2{)}^2}{(A_1-A_2{)}^2}=\frac{(4+3{)}^2}{(4-3{)}^2}=\frac{49}{1}$