Decibels, pressure & displacement amplitudes

In summary, the conversation discusses the calculation of linear sound intensity, pressure amplitude, and displacement amplitude of a jackhammer emitting sound at 130 dB and with a wavelength of 1.0 m. The equation Beta = 10 log (I / Io) is used to solve for the linear sound intensity. The pressure amplitude can be calculated using a lengthy equation involving speed of sound, density of air, and frequency or wavelength of the sound. The displacement amplitude can be found by using the frequency of the soundwave, which is equal to the speed of sound divided by the wavelength.
  • #1
heartofaragorn
33
0

Homework Statement


A jackhammer emits sound at a decibel level of 130 dB. The wavelength of the sound is 1.0 m. What is the linear sound intensity? What is the pressure amplitude? What is the displacement amplitude?


Homework Equations


Beta = 10 log (I / Io)
...and??


The Attempt at a Solution


Solved for question 1, the linear sound intensity, and received an answer of 10 Watts/meter. I combed my physics text and have not found an equation that wil provide me with either the pressure or displacement amplitude based upon the information I am given. I found a lengthy equation using density, angular velocity, and some variable "s naught" among other variables, and I simply don't have this information or have little means of finding it. Could someone please just help me find the right equations?? Thank you!
 
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  • #2
heartofaragorn said:

Homework Statement


A jackhammer emits sound at a decibel level of 130 dB. The wavelength of the sound is 1.0 m. What is the linear sound intensity? What is the pressure amplitude? What is the displacement amplitude?


Homework Equations


Beta = 10 log (I / Io)
...and??


The Attempt at a Solution


Solved for question 1, the linear sound intensity, and received an answer of 10 Watts/meter. I combed my physics text and have not found an equation that wil provide me with either the pressure or displacement amplitude based upon the information I am given. I found a lengthy equation using density, angular velocity, and some variable "s naught" among other variables, and I simply don't have this information or have little means of finding it. Could someone please just help me find the right equations?? Thank you!

I think that lengthy equation is what you need. It should involve speed of sound, density of air, frequency or wavelength of the sound... The speed of sound and density of air should be given as constants in your text.
 
  • #3
Okay, I think I figured out what the pressure amplitude is...but what about the displacement amplitude? Again, I have no means (as far as I can see) of calculating omega or frequency or other factors needed to solve for the amplitude...

Please help! :)
 
  • #4
heartofaragorn said:
Okay, I think I figured out what the pressure amplitude is...but what about the displacement amplitude? Again, I have no means (as far as I can see) of calculating omega or frequency or other factors needed to solve for the amplitude...

Please help! :)

Frequency of a soundwave is just speed of sound divided by wavelength... what other terms do you need?
 
  • #5
I was actually able to finally figure it out. Thanks for the help!
 

What are decibels?

Decibels (dB) are a unit of measurement used to express the relative intensity of sound. They are a logarithmic scale that compares the sound pressure level to a reference sound pressure level.

How is sound pressure measured?

Sound pressure is measured in units of pascals (Pa). It is a measure of the force exerted by sound waves on a surface. The greater the sound pressure, the louder the sound.

What is the relationship between decibels and sound pressure?

Decibels and sound pressure have a logarithmic relationship. A 10 dB increase in sound pressure corresponds to a 10-fold increase in sound intensity, and a 20 dB increase corresponds to a 100-fold increase in sound intensity.

What is the difference between pressure amplitude and displacement amplitude?

Pressure amplitude is a measure of the maximum change in sound pressure, while displacement amplitude is a measure of the maximum distance a particle in the medium moves from its resting position due to the sound wave. They are related to each other through the speed of sound in the medium.

What factors affect the decibel level of a sound?

The decibel level of a sound can be affected by the distance from the sound source, the frequency of the sound, and any obstacles or barriers that the sound waves encounter. The medium through which the sound travels can also affect the decibel level.

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