An unknown gas is introduced into the aforementioned apparatus using the same tu

Question

An unknown gas is introduced into the aforementioned apparatus using the same tuning fork, and the first resonance occurs when the air column is 5.74 cm long. Find the speed of sound in the gas. V sound = m/s A long tube open at both ends is partially submerged in a beaker of water, and a vibrating tuning fork of unknown frequency is placed near the top of the tube. The length of the air column, L, is adjusted by moving the tube vertically. The sound waves generated by the fork are reinforced when the length of the air column corresponds to one of the resonant frequencies of the tube. Suppose the smallest value of L for which a peak occurs in the sound intensity is 8.78 cm. Take the speed of sound to be 336 m/s. (a) With this measurement, determine the frequency of the tuning fork. 956.7Hz (b) Find the wavelength and the next two air-column lengths giving resonance. ? .351 m L2 = .263 m L3 = .439 m

Explanation / Answer

The fundamental frequency (or first harmonic) of an tube open at both ends is: f = v / (2·L) where v is the speed of sound and L the length of the tube. The n-th harmonic frequency is n times the first harmonic frequency: f_n = n · f. Hence the difference of the frequencies any two successive harmonics equals the fundamental frequency. For this tube: f = 315s?¹ - 280s?¹ = 35s?¹ with the formula for the fundamental frequency you get the speed of sound: v = 2·L·v = 2 · 2.0m · 35s?¹ = 140m/s

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