Question

Two sound waves travelling in the same direction are represented by equations $Y_1=A_{1}Sin504\pi t$; $Y_2=A_{2}Sin512\pi t$. These two sound waves superpose to produce beats. The intensity of sound changes from minimum to maximum in a time of

• A. 1/2 s
• B. 1/4s
• C. 1/8 s
• D. 1/16 s

Answer 1

The correct option is C 1/8 s

$y_1=A_{1}sin\left(504\pi t\right)$

$y_2=A_{2}sin\left(512\pi t\right)$

$beat={\delta }_2-{\delta }_1$$=\frac{{\omega }_2}{2\pi }-\frac{{\omega }_1}{2\pi }$$=\frac{512\pi }{2\pi }-\frac{504\pi }{2\pi }$$=4$

Time to go form minimum to maximum intensity is $\frac{1}{2}\times \frac{1}{beat}$

$=\frac{1}{2}\times \frac{1}{4}$

$=\frac{1}{8}second$