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?

검증된 단계별 안내

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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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

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.