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An air column in a pipe, which is closed at one end, will be in resonance with a vibrating tuning fork of frequency 264 Hz if the length of the column in cm is (a) 31.25 (b) 62.50 (c) 93.75 (d) Both (a) & (c)

An air column in a pipe, which is closed at one end, will be in resonance with a vibrating tuning fork of frequency 264 Hz if the length of the column in cm is

(a) 31.25
(b) 62.50
(c) 93.75
(d) Both (a) & (c)

Grade:Upto college level

1 Answers

Vikas TU
14149 Points
3 years ago
Natural frequencies of a pipe of length ll, closed at one end, are given by, ν=nv/(4l)ν=nv/(4l), where v=330m/sv=330m/s is the speed of sound and nn is an odd integer. Thus, the possible length of pipe (closed at one end) that can resonate with a tuning fork of frequency ν=264Hzν=264Hz are,
ln=nv4ν=n(330)4(264)=0.3125nm,
ln=nv4ν=n(330)4(264)=0.3125nm,
which gives l1=31.25cml1=31.25cm, l3=93.75cml3=93.75cm, l5=156.25cml5=156.25cm
 

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