Question

A popular car stereo has four speakers, each rated at 60 W. In answering the following questions, assume that the speakers produce sound at their maximum power.

A) Find the intensity I of the sound waves produced by one 60-Wspeaker at a distance of 1.0 m.

Answer: 4.8 W/m^2

B) Find the intensity I of the sound waves produced by one 60-Wspeaker at a distance of 1.5 m.

Answer: 2.1 W/m^2

C) Find the intensity I of the sound waves produced by four 60-Wspeakers as heard by the driver. Assume that the driver is located 1.0 m from each of the two front speakers and 1.5 m from each of the two rear speakers.

Answer: 13.8 W/m^2

D)The threshold of hearing is defined as the minimum discernible intensity of the sound. It is approximately 10^(-12) W/m2. Find the distance dfrom the car at which the sound from the stereo can still be discerned. Assume that the windows are rolled down and that each speaker actually produces 0.06 W of sound, as suggested in the last follow-up comment.

d= ___.

Answer 1

A) Intensity: $4.8 W/m^2$

B) Intensity: $2.1 W/m^2$

C) Total intensity: $13.8 W/m^2$

D) Distance: $1.38\cdot 10^5 m$

Explanation:

A)

The relationship between intensity of a sound and power emitted is given by

$I=\frac{P}{A}$

where

I is the intensity

P is the power

A is the surface area at the distance considered

For the speaker in this problem:

P = 60 W

The distance is r = 1.0 m, so the area to consider is the surface of a sphere with this radius:

$A=4\pi r^2 = 4\pi(1.0)^2=12.6 m^2$

Therefore, the intensity is

$I=\frac{60}{12.6}=4.8 W/m^2$

B)

For this problem, we can use the same equation we used before:

$I=\frac{P}{A}$

where in this case, we have:

P = 60 W is the power of the speaker

r = 1.5 m is the distance considered

Therefore, the area of the spherical surface is

$A=4\pi r^2 = 4\pi(1.5)^2=28.3 m^2$

And so, the intensity here is

$I=\frac{60}{28.3}=2.1 W/m^2$

C)

In this problem, we have to consider 4 speakers. In order to find the total intensity, we have to add the intensity of each speakers.

For the two front speakers, we have

$P=60 W$

r = 1.0 m

So we have already calculated their intensity in part A), and it is

$I_1 = I_2 = 4.8 W/m^2$

For the two rear speakers, we have

$P=60 W$

r = 1.5 m

So their intensity has been calculated in part B),

$I_3 = I_4 = 2.1 W/m^2$

Therefore, the total intensity is

$I=I_1 + I_2 + I_3 + I_4 = 4.8+4.8+2.1+2.1=13.8 W/m^2$

D)

In this case, we want to find the distance r at which the intensity is

$I=10^{-12} W/m^2$

Using four speakers with power

P = 0.06 W

Since we have 4 speakers, the intensity due to each speaker at the location considered must be

$I'=\frac{I}{4}=\frac{10^{-12}}{4}=2.5\cdot 10^{-13} W/m^2$

Using the usual equation, we find the area:

$A=\frac{P}{I'}=\frac{0.06}{2.5\cdot 10^{-13}}=2.4\cdot 10^{11} m^2$

And so, we can find what is the corresponding distance:

$A=4\pi r^2\\r=\sqrt{\frac{A}{4\pi}}=\sqrt{\frac{2.4\cdot 10^{11}}{4\pi}}=1.38\cdot 10^5 m$

So, the person must be at 138 km.

Learn more about sound waves:

brainly.com/question/4899681

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