Two small speakers emit sound saves of different frequencies. Speaker A has an o

Question

Two small speakers emit sound saves of different frequencies. Speaker A has an output of 0.60 mW and speaker B has an output of 1.70 mW. (a) Determine the sound level (in decibels) at point C (Fig. P17.31) if only speaker A emits sound. 82.81 Your response differs from the correct answer by more than 10%. Double check your calculations. dB (b) Determine the sound level (in decibels) at point C if only speaker B emits sound. dB (c) Determine the sound level (in decibels) at point C if both speakers emit sound. dB

Explanation / Answer

a)

The distance AC is

AC=sqrt[32+42]=5 m

If only speaker A emits sound ,then sound intensity at Point C is given by

I=P/4pi*AC2 =(0.6*10-3)/(4pi*52) =1.91*10-6 W/m2

The Sound level at point C in dB is given by

BC=10Log(I/Io)=10Log(1.91*10-6/10-12)

BC=62.81 dB

b)

The Distance BC is

BC=sqrt[22+42]=4.472 m

If only speaker B emits sound ,then sound intensity at Point C is given by

I=P/4pi*BC2 =(1.7*10-3)/(4pi*4.4722) =6.764*10-6 W/m2

The Sound level at point C in dB is given by

BC=10Log(I/Io)=10Log(6.764*10-6/10-12)

BC=68.3 dB

c)

If both speakers are working ,then sound level in dB a point C is

B=62.81+68.3=131.11 dB

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