Question
Five people talk simultaneously. If the intensity level is 70 dB when either one speaks alone, what is the intensity level when both speak at once?
Answers
Joshua
a) Intensity from 1 person = i, from 5 people = 5i, reference level = iₒ
dB = 10 log (i / iₒ)
For 1 person .. 97 = 10 log (i/iₒ) .. log (i/iₒ) = 9.7 .. i /iₒ = 10^9.7 .. .. i = iₒ x 10^9.7
For 5 people .. i' = 5 i .. .. i' = 5 iₒ x 10^9.7..
dB = 10 log (i' / iₒ)
dB = 10 log (5 iₒ x 10^9.7 / iₒ)
dB = 10 log (5 x 10^9.7) .. 10 log (5 x 5.01^9) .. 10 log (2.506^10) .. 10 x 10.39
Total intensity ►= 104 dB .. .. (103.9 dB)
b)
F' = frequency that arrives at insect (source [Vs] moving towards insect)
F'= Vo x Fo / (Vo - Vs)
F' = 340m/s x 60.60kHz / (340m/s - 4.70m/s) .. .. F' = 61.45 kHz
F'' = frequency received by bat moving [Vr] towards stationary source F' (reflected by insect)
F'' = (Vo + Vr)F' / Vo
F'' = (340 + 4.70) x 61.45kHz / 340 .. .. .. ►F'' = answer 62.30 kHz
dB = 10 log (i / iₒ)
For 1 person .. 97 = 10 log (i/iₒ) .. log (i/iₒ) = 9.7 .. i /iₒ = 10^9.7 .. .. i = iₒ x 10^9.7
For 5 people .. i' = 5 i .. .. i' = 5 iₒ x 10^9.7..
dB = 10 log (i' / iₒ)
dB = 10 log (5 iₒ x 10^9.7 / iₒ)
dB = 10 log (5 x 10^9.7) .. 10 log (5 x 5.01^9) .. 10 log (2.506^10) .. 10 x 10.39
Total intensity ►= 104 dB .. .. (103.9 dB)
b)
F' = frequency that arrives at insect (source [Vs] moving towards insect)
F'= Vo x Fo / (Vo - Vs)
F' = 340m/s x 60.60kHz / (340m/s - 4.70m/s) .. .. F' = 61.45 kHz
F'' = frequency received by bat moving [Vr] towards stationary source F' (reflected by insect)
F'' = (Vo + Vr)F' / Vo
F'' = (340 + 4.70) x 61.45kHz / 340 .. .. .. ►F'' = answer 62.30 kHz