A variable-length air column is placed just below a vibrating wire that is fixed at the both ends. The length of air column open at one end is gradually increased from zero until the first position of resonance is observed at 20 cm. The wire is 115.4 cm long and is vibrating in its third harmonic.

Question

A variable-length air column is placed just below a vibrating wire that is fixed at the both ends. The length of air column open at one end is gradually increased from zero until the first position of resonance is observed at 20 cm. The wire is 115.4 cm long and is vibrating in its third harmonic.
Find the speed of transverse waves in the wire if the speed of sound in air is 340 m/s. Answer in units of m/s.

bobpursley · Answer

open one end, acoustic length of tube must be 1/4 lambad

sound wavelength=.80meters

frequency=340/.8 hz

now, you know the length of the wire is 3/2 lambda

frequency(lambda)=speed
solve for speed on the wire.