If the air column in a pipe which is closed at one end, is in resonance with a vibrating tuning fork at a frequency 260 Hz, then the length of the air column is

Question

If the air column in a pipe which is closed at one end, is in resonance with a vibrating tuning fork at a frequency 260 Hz, then the length of the air column is (A) 35.7 cm (B) 31.7 cm (C) 12.5 cm (D) 62.5 cm

Tardigrade Admin · Accepted Answer

Frequency of the tuning fork, v=260 Hz The fundamental frequency of a closed organ pipe is v=(v/4 L) where v is the velocity of sound in air. ∴ Length of air column is L=(v/4(v))=(330/4 × 260)=31.7 cm

Q. If the air column in a pipe which is closed at one end, is in resonance with a vibrating tuning fork at a frequency $260 Hz$ , then the length of the air column is

35.7 cm

31.7 cm

12.5 cm

62.5 cm

Frequency of the tuning fork, $v = 260 Hz$
The fundamental frequency of a closed organ pipe is $v = \frac{v}{4 L}$
where $v$ is the velocity of sound in air.
$∴$ Length of air column is $L = \frac{v}{4 ( v )} = \frac{330}{4 \times 260} = 31.7 c m$

Q. If the air column in a pipe which is closed at one end, is in resonance with a vibrating tuning fork at a frequency 260Hz, then the length of the air column is