Ch 16: Sound & Hearing

Young & Freedman Calc - University Physics 14th Edition

Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610Non è quello che usi tu?Cambia libro di testo

Young & Freedman Calc 14th Edition

Ch 16: Sound & Hearing

Problema 14

Capitolo 16, Problema 14

(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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Step 1: Understand the relationship between sound intensity level (in decibels) and sound intensity. The sound intensity level in decibels is given by the formula:

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

₀, where

I

is the sound intensity and

I

₀ is the reference intensity.

Step 2: To find the factor by which the sound intensity must be increased, use the change in sound intensity level formula:

ΔL = 10 \log I

_fI_i, where

I

_f is the final intensity and

I

_i is the initial intensity.

Step 3: Set

ΔL

to 13.0 dB and solve for the ratio

I

_fI_i. This gives:

13 = 10 \log I

_fI_i.

Step 4: Rearrange the equation to solve for the intensity ratio:

I

_fI_i=101310. This expression gives the factor by which the intensity must be increased.

Step 5: For part (b), understand that the change in sound intensity level is independent of the original intensity because the decibel scale is logarithmic. The factor by which intensity changes depends only on the difference in decibels, not the initial value.

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Sound Intensity Level

Sound intensity level, measured in decibels (dB), is a logarithmic scale that quantifies the intensity of sound relative to a reference level. It is calculated using the formula L = 10 log10(I/I0), where I is the sound intensity and I0 is the reference intensity, typically the threshold of hearing. This scale allows for easier comparison of sound intensities.

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Sound Intensity Level and the Decibel Scale

Logarithmic Scale

A logarithmic scale is a nonlinear scale used for a large range of quantities. In the context of sound intensity, it means that each increase of 10 dB represents a tenfold increase in intensity. This property is crucial for understanding how changes in dB relate to changes in actual sound intensity, allowing for calculations without needing the original intensity value.

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Sound Intensity Level and the Decibel Scale

Sound Intensity

Sound intensity refers to the power per unit area carried by a sound wave, typically measured in watts per square meter (W/m²). It is a physical quantity that describes the energy of sound waves passing through a given area, and is directly related to the perceived loudness of the sound. Understanding sound intensity is essential for calculating changes in sound intensity levels.

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Sound Intensity Level and the Decibel Scale

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