Question

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 ______.

Options

• 360 Hz

• 420 Hz

• 480 Hz

• 600 Hz

Answer 1

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 420 Hz.

Explanation:

Resonate frequencies are n_1​v and n_2​v.

where n_1​ and n₂​ are integers and v is fundamental frequency.

Here, n₁v = 180 Hz and n₂v = 300 Hz 

∴ `"n"_1/"n"_2=180/300=18/30=3/5`

∴ 3v = 180 or v = `180/3` = 60 Hz

Possible harmonics in the case of closed end organ pipe are 1, 3, 5, 7, 9, 11, 13, …

The corresponding frequencies are 60 Hz, 180 Hz, 300 Hz, 420 Hz, ……