Ratio of Intensities of 2 sounds

In summary, the decibel scale of loudness is L = 10 log##\frac{I}{Io}## where I, measured in watts per square meter, is the intensity of the sound and Io= ##10^-12## watt/m 2 is the softest audible sound at 1000 hertz. Classical music typically ranges from 30 to 100 decibels. The human ear's pain threshold is about 120 decibels. The ratio of the intensities of the two sounds is 7 when a jet engine at 50 meters has a decibel level of 130 and a normal conversation at 1 meter has a decibel level of 60.
  • #1
Irishdoug
102
16

Homework Statement


The decibel scale of loudness is L = 10 log##\frac{I}{Io}## where I, measured in watts per square meter, is the intensity of the sound and Io= ##10^-12## watt/m 2 is the softest audible sound at 1000 hertz. Classical music typically ranges from 30 to 100 decibels. The human ear's pain threshold is about 120 decibels.

Suppose that a jet engine at 50 meters has a decibel level of 130, and a normal conversation at 1 meter has a decibel level of 60. What is the ratio of the intensities of the two sounds?

Homework Equations


L = 10 log ##\frac{I}{Io}## where Io is ##10^{-12}## and I is the intensity of the sound in square meters.

The Attempt at a Solution


Let I1 be intensity of jet engine and I2 intensity of converstaion.

log##\frac{I1}{Io}##/ ##\frac{I2}{Io}## = log##\frac{I1}{Io}## - log##\frac{I2}{Io}##

= log##\frac{130}{10^-12}## - log##\frac{60}{10^-12}##

I thought this would give correct answer however it did not. The correct answer is 13 - 6 = 7, s0 ##\frac{I1}{I2} =## ##10^7##

I then tried plugging in numbers in various ways but cannot get the correct answer. ANy idea what I have done wrong?
 
Physics news on Phys.org
  • #2
From the definition, (ratios of) intensities should be "fed" to the log function, and decibels are what comes out. In your equations, the log function seems to be "fed" with the decibels...
 
  • #3
Sorry I don't quite follow?
 
  • #4
On the last line, there are 130 and 60 decibels under the log function... Instead, according to definition, log function should be applied to intensities, and decibels produced as a result...
 
  • Like
Likes Irishdoug
  • #5
Suppose that a jet engine at 50 meters has a decibel level of 130...

Equation ##L = \log(I/I_0)## relates ##I## in W/m##^2## to ##L## in dB. You're given a number in dB. So which variable in that equation are you being given?
 
  • Like
Likes Irishdoug
  • #6
Thanks for replies. I'll give it another go tonight.
 

Related to Ratio of Intensities of 2 sounds

What is the ratio of intensities of 2 sounds?

The ratio of intensities of 2 sounds refers to the relative difference in loudness between two sounds. It is typically measured in decibels (dB), and can range from 0 dB (no difference) to infinity (one sound is significantly louder than the other).

How do you calculate the ratio of intensities of 2 sounds?

The ratio of intensities can be calculated by taking the logarithm of the intensity of one sound and subtracting it from the logarithm of the intensity of the other sound. This can be represented by the equation: Ratio = log(I1) - log(I2), where I1 and I2 are the intensities of the two sounds.

What factors can affect the ratio of intensities of 2 sounds?

The ratio of intensities can be affected by various factors such as distance from the source of the sound, the direction of the sound, the frequency of the sound, and the presence of any barriers or obstacles between the two sounds.

Why is the ratio of intensities important in sound measurement?

The ratio of intensities is important in sound measurement because it allows us to accurately compare the loudness of two sounds. It takes into account the logarithmic nature of human perception of sound and provides a more meaningful representation of the difference in loudness between sounds.

How can the ratio of intensities be used in practical applications?

The ratio of intensities is commonly used in various fields such as acoustics, engineering, and psychology. It can help in determining the minimum audible difference between sounds, evaluating the effectiveness of noise control measures, and studying the perception of sound in different environments.

Similar threads

  • Introductory Physics Homework Help
Replies
4
Views
1K
  • Introductory Physics Homework Help
Replies
4
Views
5K
  • Introductory Physics Homework Help
Replies
2
Views
2K
  • Introductory Physics Homework Help
Replies
2
Views
767
  • Introductory Physics Homework Help
Replies
4
Views
1K
  • Introductory Physics Homework Help
Replies
4
Views
4K
  • Introductory Physics Homework Help
Replies
9
Views
7K
  • Introductory Physics Homework Help
Replies
8
Views
4K
  • Introductory Physics Homework Help
Replies
8
Views
2K
  • Introductory Physics Homework Help
Replies
1
Views
975
Back
Top