Question

A pipe 20 cm long is closed at one end. Which harmonic mode of the pipe is resonantly excited by a soure of 1237.5 Hz? (sound velocity in air `=330ms^(-1))`

Answer 1

Length of pipe

`" " l=20cm=20xx10^(-2)m`
`" " v_("funda")=(v)/(4L)=(330)/(4xx20xx10^(-2))" "` (for closed pipe)
`" " v_("funda")=(330xx100)/(80)=412.5Hz `
`" " (v_("given"))/(v_("funda"))=(1237.5)/(412.5)=3`
Hence, 3rd harmonic node of the pipe is resonantly excited by the sourece of given frequency.