At a rock concert, a dB meter registered 126 dBwhen placed 2.1 m in front of a l

Question

At a rock concert, a dB meter registered 126 dBwhen placed 2.1 m in front of a loudspeaker on the stage. The intensity of the reference level required to determine the sound level is 1.0×1012W/m2.

Part A

What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?

Express your answer to two significant figures and include the appropriate units.

Part B

How far away would the sound level be 84 dB?

Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

Given that

Intenisty level (beta) =126dB

The intensity of the reference level required to determine the sound level is (I0) =1.0×1012W/m2.

We know that formula for sound level intenisty is given by

Beta =10log(I/Io)

126dB =10log(I/1.0×1012W/m2.)

12.6 =log(I/1.0×1012W/m2)

now by simplifying the above equation we get

I =(1012.6)(1.0×1012W/m2.) =100.6W/m2 =3.98W/m2

The intenisty of sound is given by

I =P/4pir2

the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air is given by

P =I(4pir2) =(4*3.14*(2.1)2)*(3.98W/m2)=220.450W

b)

Given that

Beta =84dB

Now from the above formula

84dB =10log(I/1.0×1012W/m2)

I/1.0×1012W/m2)=108.4

I =108.4*(1.0×1012W/m2)=251188643.151*10-12W/m2=2.511*10-4W/m2

Now I =P/4pir2

r =Sqrt(P/4piI) =Sqrt(220.450W/4*3.14*2.511*10-4W/m2) =264.385m

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.