How far can your voice carry at 40 dB?

In summary, the conversation discusses how to calculate the lowest decibel at which to shout a greeting in a park to be heard by a friend 100 m away. The correct answer is 40 dB, which can be found by using the equation β = 10log(I/Io) and considering the sound intensity at a certain radius from the source. The conversation also mentions the challenge of not having a baseline to compare the 100 m distance to and suggests working backwards to find the solution.
  • #1
Kavorka
95
0
You are in a park when you spot your friend 100 m away. At what lowest decibel should you shout your greetings so that your friend can just hear you? Assume that your friend has normal hearing.

My prof never gave an example of how to do this and I can't figure it out. The correct answer is 40 dB. We know that β = 10log(I/Io) and I = P/A = P/4∏r^2

I really just have no idea how to do this because they gave no baseline to compare the 100 m distance to.
 
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  • #2
It might hinge on a person's ability to just barely discern a change in sound of 1dB. But that still won't get me to a solution.

Maybe try working backwards. If it's 1dB at 100m radius, at what radius is it 40dB?
 

1. What is sound intensity measured in decibels?

Sound intensity is measured in decibels (dB), which is a logarithmic unit used to quantify the intensity or loudness of a sound. It is based on a scale from 0 dB (threshold of hearing) to about 140 dB (threshold of pain).

2. How is sound intensity decibels calculated?

The formula for calculating sound intensity in decibels is: dB = 10 log (I/I0), where I is the intensity of the sound and I0 is the reference intensity (usually 10-12 watts per square meter).

3. What is the relationship between sound intensity and decibels?

The relationship between sound intensity and decibels is logarithmic, meaning that a small increase in sound intensity will result in a larger increase in decibels. For example, a sound with an intensity of 10 times the reference intensity will be 10 decibels louder.

4. What is the range of decibels that the human ear can hear?

The human ear can typically hear sounds ranging from 0 dB, the threshold of hearing, to about 140 dB, the threshold of pain. However, prolonged exposure to sounds above 85 dB can cause hearing damage.

5. How does sound intensity decibels affect human hearing?

The higher the decibel level, the louder the sound and the greater the potential for damage to the human ear. At 85 dB, prolonged exposure can lead to hearing loss. At 120 dB, even short exposure can cause permanent damage.

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