A) 306 m/s
B) 331 m/s
C) 340 m/s
D) 360 m/s
Correct Answer: A
Solution :
Number of beats = 12/s \[{{n}_{1}}-{{n}_{2}}=12\] \[or\frac{v}{{{\lambda }_{1}}}-\frac{v}{{{\lambda }_{2}}}=12\] \[orv\,\left( \frac{{{\lambda }_{2}}-{{\lambda }_{1}}}{{{\lambda }_{1}}{{\lambda }_{2}}} \right)=12\] or \[v=\frac{12{{\lambda }_{1}}\,{{\lambda }_{2}}}{{{\lambda }_{2}}-\,{{\lambda }_{1}}}\] Given \[{{\lambda }_{1}}=50\,cm=0.50\,m\] \[{{\lambda }_{2}}=51\,cm=0.51\,m\] \[\therefore v=speed\,of\,sound\] \[=\frac{12\times 0.50\times 0.51}{(0.51-0.50)}\] \[=\frac{12\times 0.50\times 0.51}{0.01}=306\,m/s\] Thus, speed of sound is 306 m/s.
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