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Q.
An organ pipe closed at one end resonates with a tuning fork of frequencies $180\, Hz$ and $300\, Hz$. It will also resonate with tuning fork of frequency
Waves
Solution:
Resonate frequencies are $n_{1} v$ and $n_{2} v$.
where $n_{1}$ and $n_{2}$ are integers and $v$ is fundamental frequency.
Here, $n_{1} v=180\, Hz$ and $n_{2} v=300\, Hz$
$\therefore \,\,\,\,\frac{n_{1}}{n_{2}}=\frac{180}{300}=\frac{18}{30}=\frac{3}{5}$
$\therefore \,\,\,\, 3 v=180\,\,\,$ or $\,\,\,v=\frac{180}{3}=60 \,Hz$
Possible harmonics in the case of closed end organ pipe are $ 1 ,3,5,7,9,11,13, \ldots$
The corresponding frequencies are $60 \,Hz , 180\, Hz , 300 \,Hz, 420\, Hz , \ldots \ldots$