Sound intensity - the threshold of pain

In summary, the question asks how much closer you can move towards a sound source that is radiating sound waves uniformly in all directions before reaching the threshold of pain intensity of 1.0W/m^2. By using the formula r2 = r1(I1/I2)^1/2, it is determined that the distance to obtain an intensity of 1.0W/m^2 is 2.5m. Therefore, moving 5 more meters towards the source will result in an intensity of 1.0W/m^2, reaching the threshold of pain.
  • #1
clope023
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[SOLVED] sound intensity - the threshold of pain

Homework Statement



You are investigating the report of a UFO landing in an isolated portion of New Mexico, and encounter a strange object that is radiating sound waves uniformly in all directions. Assume that the sound comes from a point source and that you can ignore reflections. You are slowly walking toward the source. When you are 7.5 m from it, you measure its intensity to be 0.11 W/m^2.

An intensity of 1.0W/m^2 is often used as the "threshold of pain". How much closer to the source can you move before the sound intensity reaches this threshold?

Homework Equations



I1/I2 = r2^2/r1^2

The Attempt at a Solution



r2 = r1(I1/I2)^1/2

= (7.5)(.11)^1/2 = 2.5m - incorrect

done another way

r2 = [(r1)^2(I1/I2)]^1/2 = (56m^2(.11))^1/2 = 2.5m - incorrect

I dont' know the equations aren't working for me, any help is appreciated.
 
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  • #2
You are doing the right thing. I get 2.48m. All I can think of is to check the number of significant figures they (or it) are expecting. Also note that the question is asking 'how much closer can you get'. Maybe they want you to say 5m closer?
 
  • #3
Dick said:
You are doing the right thing. I get 2.48m. All I can think of is to check the number of significant figures they (or it) are expecting. Also note that the question is asking 'how much closer can you get'. Maybe they want you to say 5m closer?

yeah that was it apparently, the distance to obtain an intensity of 1W/m^2 is 2.5m and the intensity of .11W/m^2 was 7.5 so you travel 5 more meters to get within 2.5m of the threshold of pain's intensity, thanks for the hint.
 

FAQ: Sound intensity - the threshold of pain

1. What is sound intensity and how is it measured?

Sound intensity is the amount of energy that passes through a unit area in a specific direction. It is measured in decibels (dB), which is a logarithmic scale that compares the sound intensity to a reference level. The threshold of pain is typically around 120 dB.

2. How does sound intensity affect our hearing?

Sound intensity can have both positive and negative effects on our hearing. At low levels, it allows us to hear and understand sounds. However, at high levels, it can cause permanent damage to the delicate structures of our inner ear, leading to hearing loss or even deafness.

3. What is the threshold of pain and why is it important?

The threshold of pain is the sound intensity level at which a person experiences pain or discomfort. It is important because it serves as a warning sign that the sound is potentially harmful and can cause damage to our hearing if we continue to be exposed to it.

4. How is the threshold of pain different for different individuals?

The threshold of pain can vary from person to person depending on factors such as age, gender, and overall health. Younger individuals tend to have a lower threshold of pain, while older individuals may have a higher threshold due to age-related hearing loss. Gender also plays a role, with males typically having a higher threshold than females.

5. Can the threshold of pain be exceeded and what are the consequences?

Yes, the threshold of pain can be exceeded. When this happens, it can cause temporary or permanent damage to our hearing, including tinnitus (ringing in the ears), hyperacusis (sensitivity to sound), and noise-induced hearing loss. It is important to protect our ears and limit exposure to loud sounds to prevent these consequences.

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