Ch 16: Sound & Hearing

Young & Freedman Calc - University Physics 15th Edition

Young & Freedman Calc15th EditionUniversity PhysicsISBN: 9780135159552당신이 사용하는 게 아니라요?교과서 변경

Young & Freedman Calc 15th Edition

Ch 16: Sound & Hearing

문제 13

16장, 문제 13

You are trying to overhear a juicy conversation, but from your distance of 15.0 m, it sounds like only an average whisper of 20.0 dB. How close should you move to the chatterboxes for the sound level to be 60.0 dB?

검증된 단계별 안내

Understand that sound intensity level in decibels (dB) is a logarithmic measure of the intensity of a sound relative to a reference level. The formula to convert intensity to decibels is:

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

, where

I

is the intensity of the sound and

I ref

is the reference intensity.

Recognize that the intensity of sound decreases with distance according to the inverse square law:

I \approx \frac{P}{r^{2}}

, where

P

is the power of the sound source and

r

is the distance from the source.

Set up the equation for the initial condition at 15.0 m with a sound level of 20.0 dB:

20 = 10 \log (\frac{I}{I})

. Solve for

I

Set up the equation for the desired condition at a new distance

r

with a sound level of 60.0 dB:

60 = 10 \log (\frac{I}{I})

. Solve for

I

Use the inverse square law to relate the two intensities and distances:

\frac{I}{I} = \frac{r^{2}}{r^{2}}

. Solve for the new distance

r

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

주요 개념

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

Decibel Scale

The decibel (dB) scale is a logarithmic unit used to measure sound intensity. It quantifies sound levels relative to a reference level, typically the threshold of hearing. A change of 10 dB represents a tenfold change in intensity, making it crucial for understanding how sound levels increase or decrease with distance.

Inverse Square Law

The inverse square law states that the intensity of sound decreases with the square of the distance from the source. This principle is essential for calculating how sound intensity changes as you move closer or farther from the source, helping to determine the necessary distance to achieve a desired sound level.

Sound Intensity and Distance

Sound intensity is the power per unit area carried by a sound wave. As you move closer to a sound source, the intensity increases, and the perceived loudness rises. Understanding the relationship between sound intensity and distance is key to solving problems involving changes in sound levels due to movement.