The sound produced by the loudspeaker in the figure below has a frequency of 102

Question

The sound produced by the loudspeaker in the figure below has a frequency of 10200Hz and arrives at the microphone via two different paths. The sound travels through the left tube LXM, which has a fixed length. Simultaneously, the sound travels through the right tube LYM, the length of which can be changed by moving the sliding section. At M, the sound waves coming from the two paths interfere. As the length of the path LYM is changed, the sound loudness detected by the microphone changes. When the sliding section is pulled out by 0.0193m, the loudness changes from a maximum to a minimum. Find the speed at which sound travels through the gas in the tube.

Explanation / Answer

Sound speed in the tube is calculated by multiplying the frequency v by the wavelength . The trick here is calculating the wavelength.

As the sound loudness changed from a maximum to a minimum, then we know the sound interference in the case changed from constructive interference (the two sound waves are in phase, i.e. peaks are in a line with peaks and so the troughs), to a destructive interference (peaks coinciding with troughs). The least distance change required to cause such a change is a half wavelength distance, so:

/2 = 0.0193 m

= 0.0386m

Speed = v X = 10200 X 0.00386= 393.72 m/s

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