Decibels and Sound
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Question: You are at a party with your four closest friends, Alice, Bob, Charlie, and Eve. Music is playing in the background very softly you hear it at a level of 35 dB. All of your friends are talking at once and given their volume and your proximity to them you hear Alice at 45 dB, Bob at 42 dB, Eve at 48 dB and Charlie talking at 45 dB. For the purposes of this problem assume all sounds are in the same range of frequencies and all sounds are received in phase with each other. Assume all sounds are in the band defined as 300 Hz to 3000 Hz. 7
a) Convert all 5 sound sources to their absolute ratio to the power of the softest sound a human can hear (S).
b) Charlie is the "signal" you are trying to hear. Calculate the signal to noise ratio (SNR) as a unit less number.0
c) What is the bandwidth of the communication channel?
d) What is the channel capacity of the communication channel with Charlie?
e) If everyone stopped talking except Charlie what is the new channel capacity?
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Solution Summary
This solution discusses the topics of decibels linked to sound, and contains step-by-step calculations to convert decibels to softest sound a human can hear, signal to noise ratio, bandwidth of communication channel, and channel capacity of communication channel. Brief explanations are included for further topic understanding.
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(a) In terms of the softest sound a human can hear, S:
Music = 10^3.5 S:3162 S
Alice = 10^4.5 S:31623 S
Bob = 10^4.2 S:15849 S
Eve = 10^4.8 S:63096 S
Charlie = 10^4.5 S:31623 S
(b)
Signal = ...
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