3. Each time when I start lecturing I have to wait a while for the noise in the

Question

3. Each time when I start lecturing I have to wait a while for the noise in the room to decrease to a reasonable level. If just a student is talking, the sound level will be approximately 55 dB. (a What is the sound level in the room if all 18 students are talking? (b) What should he the intensity of the sound emitted by the teacher in order to exceed this noise by 50 dB? (This will make this voice to be heard by everybody in the room) (c) What power should he put in his voice in order to deliver this intensity level at a distance of 5 m? Assume that the sound radiates uniformly in all directions.) The hearing threshold is Io = 10^-12 W/m^2.

Explanation / Answer

a)

for each student intensity is I

then for 18 student intensity is 18I

Now , in dB = 10*log(18I)

dB = 10*log(18) + 10*log(I)

dB = 67.6 dB

the sound level is 67.6 dB

b)

For the teacher ,

I = 67.6 + 50 = 117.6 dB

Now , as 117.6 = 10 * log(It/1*10^12)

taking antilog

It = 0.569 W/m^2

the intensity of the teacher is 0.569 W/m^2

c)

Now , as instensity = P/area

0.569 = P/(4*pi*5^2)

P = 178.7 W

the emiited power must be 178.7 W

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