Q. 29

Two stereo speakers are separated by a distance of 2.40 m. A person stands at a distance of 3.20 m directly in front of one of the speakers as shown in figure (16-E3). Find the frequencies in the audible range (20-2000 Hz) for which the listener will hear a minimum sound intensity. Speed of sound in air = 320 m/s.



Answer :

Given:


Capture.PNG
Distance between the two speakers
d = 2.40 m
Speed of sound in air
v = 320 m/sec
Frequency of the two stereo speakers
f =?


As shown in the figure, the path difference between the sound waves reaching the listener is given by:




Wavelength of either sound wave:



We know that destructive interference will occur if the path difference is an odd integral multiple of the wavelength.


So,







On putting the value of n = 1, 2, 3,…49, the person can hear in the audible region from 20 Hz to 2000 Hz.


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