Question

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 find the length of the column ?

Answer 1

Natural frequencies of a pipe of length l, 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 oddinteger. 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