Ch 16: Sound & Hearing

Young & Freedman Calc - University Physics 14th Edition

Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610Not the one you use?Change textbook

Young & Freedman Calc 14th Edition

Ch 16: Sound & Hearing

Problem 21

Chapter 16, Problem 21

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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Sound Intensity Level and the Decibel Scale

Related Practice

Textbook Question

Standing sound waves are produced in a pipe that is 1.20 m long. For the fundamental and first two overtones, determine the locations along the pipe (measured from the left end) of the displacement nodes and the pressure nodes if the pipe is closed at the left end and open at the right end.

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)?

Textbook Question

The fundamental frequency of a pipe that is open at both ends is 524 Hz. How long is this pipe? If one end is now closed

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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.

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Textbook Question

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?

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