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1. Intro to Physics Units1h 29m
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18. Waves & Sound3h 40m
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33. Geometric Optics2h 57m
34. Wave Optics1h 15m
35. Special Relativity2h 10m

18. Waves & Sound

Sound Intensity

Physics

18. Waves & Sound

Sound Intensity

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3:42 minutes

Problem 21

Textbook Question

A baby's mouth is 30 cm from her father's ear and 1.50 m from her mother's ear. What is the difference between the sound intensity levels heard by the father and by the mother?

Verified step by step guidance

First, understand that sound intensity level is measured in decibels (dB) and is related to the intensity of sound, which decreases with distance from the source according to the inverse square law.

The formula for sound intensity level in decibels is given by:

L = 10 \log \frac{I}{I}

₀, where

I

is the intensity of the sound and

I

₀ is the reference intensity.

To find the intensity at each ear, use the inverse square law:

I = \frac{P}{4 π r^{2}}

, where

P

is the power of the sound source and

r

is the distance from the source.

Calculate the intensity at the father's ear using the distance of 30 cm (0.30 m) and at the mother's ear using the distance of 1.50 m.

Finally, find the difference in sound intensity levels by calculating the decibel levels for each intensity and subtracting them:

ΔL = L

_father-L_mother.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Sound Intensity

Sound intensity refers to the power per unit area carried by a sound wave. It is measured in watts per square meter (W/m²) and is a crucial factor in determining how loud a sound is perceived. The intensity decreases with distance from the source, following the inverse square law, meaning it diminishes as the distance increases.

Inverse Square Law

The inverse square law states that the intensity of a sound wave is inversely proportional to the square of the distance from the source. This means that as you move away from the sound source, the intensity decreases rapidly. For example, doubling the distance from the source results in a quarter of the original intensity.

Decibel Scale

The decibel scale is a logarithmic scale used to measure sound intensity levels. It allows for a more manageable representation of the wide range of sound intensities humans can perceive. A difference of 10 dB represents a tenfold change in intensity, making it easier to compare sound levels at different distances from the source.

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Related Practice

Multiple Choice

Suppose an explosion can just be heard over normal conversation with an intensity of

1.0 \times 10^{- 6} ​ {W/m}^{2}

from 10km away. At what distance from the explosion will the sound have an intensity that causes pain (

10 ​ {W/m}^{2}

)? Note that this calculation ignores absorption of sound energy by air and objects.

A speaker at a rock concert is causing you pain, so you reason the sound level must be 130dB. The speaker is 11 m away from you. To what final distance from the speaker should you move for the sound level to reach a less-painful 105 dB? Keep in mind that we are ignoring absorption of sound energy by air and objects.

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Multiple Choice

A sound wave from a police siren has an intensity of 0.01 W/m² at a certain distance. A second sound wave from an ambulance has a sound intensity level 8 dB greater than the police siren, when measured at the same distance. What is the sound intensity level (in dB) of the sound wave due to the ambulance?

(a) By what factor must the sound intensity be increased to raise the sound intensity level by 13.0 dB? (b) Explain why you don't need to know the original sound intensity

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Textbook Question

For a person with normal hearing, the faintest sound that can be heard at a frequency of 400 Hz has a pressure amplitude of about 6.0 × 10^-5 Pa. Calculate the intensity.

You live on a busy street, but as a music lover, you want to reduce the traffic noise. If, instead, you reduce the intensity by half, what change (in dB) do you make in the sound intensity level?

You live on a busy street, but as a music lover, you want to reduce the traffic noise. If you install special soundreflecting windows that reduce the sound intensity level (in dB) by 30 dB, by what fraction have you lowered the sound intensity (in W/m²)?

A sound wave in air at 20°C has a frequency of 320 Hz and a displacement amplitude of 5.00 × 10^-3 mm. For this sound wave calculate the pressure amplitude (in Pa)

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