Sound intensity distance ratio

In summary: Is the correct ratio to use for solving the problem. You can then plug in the values of dB to obtain 'I' and solve for the ratio. In summary, the ratio of the distance between Sally and the elephant to the distance between the elephant and Harry can be found by taking the ratio of their respective sound intensity levels, which are inversely proportional to the square of their distances from the source.
  • #1
raindrops
17
0

Homework Statement



Harry and Sally are sitting on opposite sides of a circus tent when and elephant trumpets a loud blast. If Harry experiences a sound intensity level of 65dB and Sally only 55dB, what is the ratio of the distance between Sally and the elephant to the distance between the elephant and Harry?

Homework Equations



I=P/(4piR^2)
B=10log(I/10^-12)

The Attempt at a Solution



65=10log(I/10^-12)
so I(harry)=10^-5.5

55=10log(I/10^-12)
so I(sally)=10^-6.5

*I have no idea where to go from here or if that was even the correct first step to take.

If I knew the Power(P), I would be able to find the radius and get distance from that, but I don't have a way to calculate that.
 
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  • #2
You don't have to know the power; it remains the same for both Harry and Sally ie dependent only on the source.
Thus we can simply obtain the relation of Intensity being inversely proportional to the square of the distance from the source. It is then a matter of using ratios to solve the problem.
 
  • #3
I'm not very good with ratios. Let me know if I did this right.

65=1/R^2 so R=.124

55=1/R^2 so R=.134

ratio is .124:.134 ?
 
  • #4
You shouldn't equate like that and solve for 'R'; its not mathematically correct. Also, are you sure you are supposed to use the dB value?

[tex]\frac{I_{Sally}}{I_{Henry}} = \frac{r_{Henry}^{2}}{r_{Sally}^{2}}[/tex]
 

Related to Sound intensity distance ratio

1. What is the sound intensity distance ratio?

The sound intensity distance ratio, also known as the inverse square law, is a principle that describes the relationship between the intensity of sound and its distance from the source. It states that as the distance from a sound source increases, the intensity of the sound decreases in proportion to the square of the distance.

2. How does sound intensity change with distance?

As the distance from the sound source increases, the sound intensity decreases. This is because sound waves spread out as they travel, causing the same amount of energy to be spread over a larger area. This results in a decrease in the sound intensity at a specific distance from the source.

3. What is the formula for calculating sound intensity distance ratio?

The formula for calculating sound intensity distance ratio is I1/I2 = (d2/d1)^2, where I1 and I2 are the sound intensities at distances d1 and d2 from the source, respectively. This formula can be used to calculate the sound intensity at a certain distance from the source based on the known sound intensity at a different distance.

4. How does sound intensity distance ratio affect sound perception?

Sound intensity distance ratio has a significant impact on how sound is perceived by the human ear. As the sound intensity decreases with distance, the sound becomes quieter and may be perceived as muffled or distant. This principle is important to consider in settings such as concerts or public announcements, where the distance between the sound source and the audience can greatly affect the perceived loudness of the sound.

5. What are some factors that can affect sound intensity distance ratio?

The sound intensity distance ratio can be affected by several factors, including the type of sound source, the medium through which the sound travels, and any obstacles or barriers between the source and the receiver. For example, sound traveling through air will experience a greater decrease in intensity compared to sound traveling through water due to the difference in density between these mediums. Additionally, objects or structures in the path of the sound can cause reflections, resulting in changes in the sound intensity at different distances.

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