Chapter 16: Q. 68 (page 453)

The sound intensity 50 m from a wailing tornado siren is
$0.10 W / m^{2}$ .
a. What is the intensity at 1000 m?
b. The weakest intensity likely to be heard over background noise is $\approx 1 μ W / m^{2}$ . Estimate the maximum distance at
which the siren can be heard.

Short Answer

Expert verified

a. Intensity of sound is, $2.5 \times 10^{- 4} W / m^{2} .$

b. The maximum distance is $16 k m$ , from which the siren can be heard.

Step by step solution

Part a Step 1: Given data

At a distance $r_{1} = 50 m$ , intensity of sound is $I_{1} = 0.10 W / m^{2}$

At a distance , $r_{2} = 1000 m$ the intensity of sound $I_{2}$ should be found.

Determination of intensity

The intensity $I_{2}$ can be obtained as,
role="math" localid="1648922739120" $\frac{I_{2}}{I_{1}} = \frac{r_{1}^{2}}{r_{2}^{2}} I_{2} = I_{1} \frac{r_{1}^{2}}{r_{2}^{2}} I_{2} = (0.10 W / m^{2}) \frac{{(50 m)}^{2}}{{(1000 m)}^{2}} I_{2} = 2.5 \times 10^{- 4} W / m^{2}$

Part b Step 1: Given data

The weakest intensity likely to be heard over background

noise is $\approx 1 μ W / m^{2}$ .

The maximum distancerole="math" localid="1648922664072" $r'$ should be obtained from which the siren can be heard.

Determination of the maximum distance

The maximum distance can be obtained by,

$\frac{I_{3}}{I_{1}} = \frac{r_{1}^{2}}{r'^{2}} r'^{2} = r_{1}^{2} \frac{I_{1}}{I_{3}} r' = \sqrt{\frac{I_{1}}{I_{3}}} r_{1} r' = \sqrt{\frac{0.10 W / m^{2}}{1 \times 10^{- 6} W / m^{2}} \times} 50 m r' = 16000 m r' = 16 k m$

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The sound intensity 50 m from a wailing tornado siren is
$0.10 W / m^{2}$ .
a. What is the intensity at 1000 m?
b. The weakest intensity likely to be heard over background noise is $\approx 1 μ W / m^{2}$ . Estimate the maximum distance at
which the siren can be heard.

Short Answer

Step by step solution

Part a Step 1: Given data

Determination of intensity

Part b Step 1: Given data

Determination of the maximum distance

One App. One Place for Learning.

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The sound intensity 50 m from a wailing tornado siren is0.10W/m2.a. What is the intensity at 1000 m?b. The weakest intensity likely to be heard over background noise is ≈1μW/m2. Estimate the maximum distance atwhich the siren can be heard.

Short Answer

Step by step solution

Part a Step 1: Given data

Determination of intensity

Part b Step 1: Given data

Determination of the maximum distance

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Engineering Physics

Mechanics and Materials

Rotational Dynamics

Energy Physics

Wave Optics

Force

Study anywhere. Anytime. Across all devices.

The sound intensity 50 m from a wailing tornado siren is
$0.10 W / m^{2}$ .
a. What is the intensity at 1000 m?
b. The weakest intensity likely to be heard over background noise is $\approx 1 μ W / m^{2}$ . Estimate the maximum distance at
which the siren can be heard.