Question

An organ pipe, open from both ends produces 5 beats per second when vibrated with a source of frequency $200$ $Hz$ in its fundamental mode. The second harmonic of the same pipe produced 10 beats per second with a source of frequency of pipe is fundamental frequency of pipe is

• A. $195$ $Hz$
• B. $205$ $Hz$
• C. $190$ $Hz$
• D. $210$ $Hz$

Answer 1

The correct option is B $205$ $Hz$

$\begin{array}{c}Initiallynumberofbeatsper\sec ond=5\\ \therefore frequencyofpipe=200\pm 5=195Hzor205Hz------\left(1\right)\\ frequencyof\sec ondharmonicsofthepipe=2nandnumberofbeatsinthiscase=10\\ \therefore 2n=420\pm 10\Rightarrow 410Hzor430Hz\\ \Rightarrow n=205Hzor215Hz-------\left(2\right)\\ fromequation\left(1\right)and\left(2\right)itisclearthatn=205Hz\end{array}$

Hence,

option $\left(B\right)$ is correct answer.