Question

An organ pipe closed at one end resonates with a tuning fork of frequencies $180Hz$ and $300Hz$. It will also resonate with tuning fork of frequency

• A. 360 Hz
• B. 420 Hz
• C. 480 Hz
• D. 600 Hz

Answer 1

Answer: (B)

Resonate frequencies are $n_{1}v$ and $n_{2}v$.
where $n_1$ and $n_2$ are integers and $v$ is fundamental frequency.
Here, $n_{1}v=180Hz$ and $n_{2}v=300Hz$
$\therefore \frac{n_1}{n_2}=\frac{180}{300}=\frac{18}{30}=\frac{3}{5}$
$\therefore 3v=180$ or $v=\frac{180}{3}=60Hz$
Possible harmonics in the case of closed end organ pipe are $1,3,5,7,9,11,13,\dots$
The corresponding frequencies are $60Hz,180Hz,300Hz,420Hz,\dots \dots$