Wave Mechanics Question 673
Question: The wavelength of two waves are 50 and 51 cm respectively. If the temperature of the room is $ 20{}^\circ C $ then what will be the number of beats produced per second by these waves, when the speed of sound at $ 0{}^\circ C $ is 332 m/s?
Options:
A) 24
B) 14
C) 10
D) none of these
Show Answer
Answer:
Correct Answer: B
Solution:
[b] $ {\lambda _{1}}=50cm. $
$ {\lambda _{2}}=51,cm. $
$ v\propto \sqrt{T}\Rightarrow \frac{v _{1}}{v _{2}}=\sqrt{\frac{T _{2}}{T _{1}}}=\sqrt{\frac{273+20}{273}} $
$ \Rightarrow ,v _{2}=319.23. $
$ v _{1}=\frac{v _{2}}{{\lambda _{1}}}=\frac{319.23}{0.50}=640Hz $
$ v _{2}=\frac{v _{2}}{{\lambda _{2}}}=\frac{319.23}{51\times {{10}^{-2}}}=625.94=626Hz. $ No. of beats $ =v _{2}-v _{1}=14Hz $
BETA
