Question

Two sound waves of wavelengths ${\lambda }_{1}and{\lambda }_2({\lambda }_2>{\lambda }_1)$ produce n beats/s, the speed of sound is

• A. $\frac{n{\lambda }_1{\lambda }_2}{{\lambda }_2-{\lambda }_1}$
• B. $n(\frac{1}{{\lambda }_1}-\frac{1}{{\lambda }_2})$
• C. $n({\lambda }_2-{\lambda }_1)$
• D. $n({\lambda }_2+{\lambda }_1)$

Answer 1

The correct option is A $\frac{n{\lambda }_1{\lambda }_2}{{\lambda }_2-{\lambda }_1}$

beats is given as $f_1-f_2$ which is given as $n$

Let the velocity of sound be $c$

using formula $c=f\lambda$

$\frac{c}{{\lambda }_1}-\frac{c}{{\lambda }_2}=n$

$c\left(\frac{{\lambda }_2-{\lambda }_1}{{\lambda }_1{\lambda }_2}\right)=n$

$c=\frac{n{\lambda }_1{\lambda }_2}{{\lambda }_2-{\lambda }_1}$