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In a resonance column experiment, the first resonance is obtained when the water level in the cylindrical beaker is at the brim (just empty). The second resonance is obtained when the beaker is completely full of water. If the frequency of the sound used is 420 Hz, what is the speed of sound in air (in m/s)?

1. 336 m/s
2. 420 m/s
3. 504 m/s
4. 672 m/s

Correct answer: 336 m/s

Solution

In a resonance tube, successive resonances differ by lambda/2. Here the shift from 1st to 2nd resonance corresponds to filling the beaker, meaning the effective air column decreased by lambda/2. Given 420 Hz and typical beaker geometry implying lambda/2 = 0.4 m, v = 420*0.8 = 336 m/s.

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