Sound Level (trouble setting up equation)

  • Thread starter Saladsamurai
  • Start date
  • Tags
    Sound
In summary, the question is asking for the multiple by which the intensity of a sound source is increased when its sound level is increased by 30 dB. The correct equation for this relationship is beta2 = beta1 + 30, where beta1 is the initial sound level and beta2 is the increased sound level. This can be solved using properties of logarithms.
  • #1
Saladsamurai
3,020
7
Sound Level and Intensity (trouble setting up equation)

A certain sound source is increased by 30 dB. By what multiple is its intensity increased?

This is what I have set up so far, but I do not think it is correct..

[tex]\beta_1=10\log\frac{I_1}{I_0}[/tex] and [tex]\beta_2=40\log\frac{I_1}{I_0}[/tex]
So,
[tex]\frac{\beta_1}{\beta_2}=\frac{10\log\frac{I_1}{I_0}}{40\log\frac{I_1}{I_0}}[/tex]

and from there I am jammed...we have been using product and sum logs so far...but this expression does not fit the bill..so I believe I have made a conceptual error in setting up the equation.

Do you see my error?
Casey
 
Last edited:
Physics news on Phys.org
  • #2
This is killing me.

Edit: I think I found the correct relationship...how about beta2=beta1+30

so beta2-beta1=30...and then I should be able to use properties of Logs......that worked.

Sweeeeeeeet.
Casey
 
Last edited:
  • #3
, it seems like you are on the right track with your equations, but there are a few things that could be clarified. Let's break down the problem step by step:

1. Sound level and intensity are related by the equation \beta=10\log\frac{I}{I_0}, where \beta is the sound level in decibels (dB), I is the intensity of the sound, and I_0 is the reference intensity (usually 10^{-12} W/m^2).

2. In this problem, we are given that the sound level is increased by 30 dB. This means that the new sound level, \beta_2, is 30 dB higher than the original sound level, \beta_1. So we can write \beta_2=\beta_1+30.

3. Now, we want to find the relationship between the intensities, I_2 and I_1, corresponding to the two sound levels. From the equation in step 1, we can write \beta_2=10\log\frac{I_2}{I_0} and \beta_1=10\log\frac{I_1}{I_0}. Substituting these into the equation from step 2, we get:

10\log\frac{I_2}{I_0}=10\log\frac{I_1}{I_0}+30

4. We can simplify this equation by dividing both sides by 10 and taking the antilog (inverse logarithm) of both sides:

\frac{I_2}{I_0}=\frac{I_1}{I_0}10^{30}

5. Now, we can see that the intensity has been increased by a factor of 10^{30}. This means that I_2 is 10^{30} times larger than I_1. So the multiple by which the intensity is increased is 10^{30}.

I hope this clarifies the problem and helps you set up the correct equation. Remember, it is always helpful to break down the problem into smaller steps and use the given information to guide your equations. Keep up the good work!
 

What is sound level?

Sound level, also known as sound pressure level, is a measure of the intensity or loudness of sound. It is measured in decibels (dB).

How is sound level measured?

Sound level is measured using a device called a sound level meter. This device measures the sound pressure level in decibels (dB) using a microphone.

What factors affect sound level?

The factors that affect sound level include the distance from the sound source, the intensity of the sound source, and the environment in which the sound is being measured (e.g. open space or enclosed room).

How do you calculate sound level?

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

What is a safe sound level?

A safe sound level is generally considered to be below 85 decibels (dB). Prolonged exposure to sounds above this level can cause hearing damage. It is recommended to use hearing protection in environments with sound levels above 85 dB.

Similar threads

  • Introductory Physics Homework Help
Replies
1
Views
789
  • Introductory Physics Homework Help
Replies
4
Views
1K
  • Introductory Physics Homework Help
Replies
4
Views
860
  • Introductory Physics Homework Help
Replies
5
Views
2K
  • Introductory Physics Homework Help
Replies
8
Views
4K
  • Introductory Physics Homework Help
Replies
3
Views
1K
  • Introductory Physics Homework Help
Replies
7
Views
1K
  • Introductory Physics Homework Help
Replies
1
Views
1K
  • Introductory Physics Homework Help
Replies
9
Views
6K
Replies
2
Views
1K
Back
Top