Each time when i start lecturing I have to wait for a noise in the room to decre

Question

Each time when i start lecturing I have to wait for a noise in the room to decrease to a reasonable level. If just a student is talking the sound level will be approximately 55dB

a) What is the sound level in the room if all 18 students are talking?

b) what should be the intensity of the sound emitted by the teacher in order to exceed the noise by 50dB?(This will make the voice to be heard by everybody in the room)

c) What power should he put in his voice in order to deliever this intensity level at a distance of 5m. ( Assume that the sound radiates uniformly in all directions). The hearing treshold is I_o=10^-12 W/m^2

Explanation / Answer

a)

let I is the intensity of one student

intensity level when one student speaks, beta = 10*log(I/Io)


when 18 students speak, beta' = 10*log(18*I/Io)

= 10*(log(I/Io) + log(18))

= 55 + 10*log(18)

= 67.55 dB

b) beta = 10*log(I/Io)

55 = 10*log(I/10^-12)

5.5 = log(I/10^-12)


I = 10^-12 * 10^5.5

I = 3.162*10^-7 W/m^2

c) I = power /Area

Power = I*area

= 3.162*10^-7*4*pi*5^2

= 9.93*10^-5 Watts

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