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150. Problem 20.35 (RHK) A large parabolic reflector having a circular opening of radius 0.50 m is used to focus sound. If the energy is delivered from the focus to the ear of a listening detective through a tube of diameter 1.0 cm with 12% efficiency, we have to find the distance away from which a whispered conversation can be understood. We can assume that the sound level of a whisper is 20 dB at 1.0 m from the source, considered to be a point, and that the threshold for hearing is 0 dB. |
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Solution: Click For PDF Version We are given that the sound level of a whisper at 1.0 m from the source is 20 dB. From this information we estimate the intensity of sound of a whisper at a distance of 1.0 m from its source. The definition of SL is
So the magnitude of I is
Therefore, the intensity of whisper sound at a distance R (m) from its source will be
The amount of energy per second picked up by the parabolic reflector of radius 0.5 m will be
We are given that sound from the focus is picked up by a tube of 1.0 cm diameter with an efficiency of 12%. Therefore, the intensity of sound received by the ear of the listener will be
If the sound is to be just audible, the condition is that its SL has to be 0 dB. This condition implies
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