Paragraph: Two plane harmonic sound waves are expressed by the equations. y_1(x, t)=A cos (0.5 π x-100 π t) y_2(x, t)=A cos (0.46 π x-92 π t) (All parameters are in MKS)Question: How many times does an observer hear maximum intensity in one second?

Q105 / 120 · JEE Advanced 2006 · Physics

Paragraph: Two plane harmonic sound waves are expressed by the equations. $$ \begin{aligned} & y_1(x, t)=A \cos (0.5 \pi x-100 \pi t) \\ & y_2(x, t)=A \cos (0.46 \pi x-92 \pi t) \end{aligned} $$ (All parameters are in MKS)Question: How many times does an observer hear maximum intensity in one second?

In one second number of maximas is called the beat frequency. Hence, $$ f_b=f_1-f_2=\frac{100 \pi}{2 \pi}-\frac{92 \pi}{2 \pi}=4 \mathrm{~Hz} $$

Hence, the correct answer is option: 'A'.