In a resonance experiment a 1025Hz tunning fork produces resonance when the air-column has length of

题目

In a resonance experiment a 1025Hz tunning fork produces resonance when the air-column has length of 24cm.Find the speed of sound,and find one other resonance length.(hint-is this first resonance?How do you know?)

答案

The tunning fork is the sound source as well as the vibration source so considering about the wave,the fork must be at the antinode of the wave and the end of the tube must be at the node of the wave.The distance between two nodes is half the wavelength,so the first resonant tube length is (lambda/4),the second one is (lambda/4+lambda/2),the third is (lambda/4+lambda/2+lambda/2)...and so on.
----------This is just estimation--------
A reasonable estimate speed of the sound is about 350m/s ,so the wavelength of sound is about 350/1025=34cm.So the first resonance length will be about 8.5cm,the second is about 26cm.
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So we believe 24cm is the second resonant length and we can do the calculation
accurately.the wavelength is 24/(3/4)=32cm,and the speed of sound is 0.32m*1025/s=328m/s.
Done!