Calculating Acoustic Pressure for 10 W/m^2 of Intensity

In summary, the formula given is: I = { (\Delta P)_{max}^2 \over 2 \rho v}, where I represents sound intensity, (\Delta P)_{max} is the maximum change in pressure, \rho is the density of air, and v is the velocity of sound. Using this formula, it can be shown that the acoustic pressure for a painful sound of 10 W/m^2 is approximately 6.5x10^-4 of an atm. This relationship can be further explored by using the accepted reference levels.
  • #1
silverdiesel
65
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The velocity of sound in air of density rho=1.29 kg/m^3 may be taken to be 330m/s. Show that the acoustic pressure for the painfull sound of 10 W/m^2 ~ 6.5x10^-4 of an atm. (atm~10^5 N/m^2)

What is acoustic pressure. This question is easy I am sure, but I don't really know what it is asking for. I have read and re-read the chapter on sound waves, but I don't see any term defined as acoustic pressure. I am guessing it is the "overpressure", but I don't know of a relationship between overpressure and Intensity.
 
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  • #2
silverdiesel said:
The velocity of sound in air of density rho=1.29 kg/m^3 may be taken to be 330m/s. Show that the acoustic pressure for the painfull sound of 10 W/m^2 ~ 6.5x10^-4 of an atm. (atm~10^5 N/m^2)

What is acoustic pressure. This question is easy I am sure, but I don't really know what it is asking for. I have read and re-read the chapter on sound waves, but I don't see any term defined as acoustic pressure. I am guessing it is the "overpressure", but I don't know of a relationship between overpressure and Intensity.
From the given information, it almost sounds like you are expected to use the speed of sound and the density of air to come up with the relationship between the reference levels of sound intensity and sound pressure. If that is the case, then it will require more than using the accepted levels. If you are allowed to use the accepted reference levels in your problem, then all you need to do is express the quantities relative to those reference levels and equate the two levels as done here

http://physics.mtsu.edu/~wmr/log_3.htm
 
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  • #3
silverdiesel said:
The velocity of sound in air of density rho=1.29 kg/m^3 may be taken to be 330m/s. Show that the acoustic pressure for the painfull sound of 10 W/m^2 ~ 6.5x10^-4 of an atm. (atm~10^5 N/m^2)

What is acoustic pressure. This question is easy I am sure, but I don't really know what it is asking for. I have read and re-read the chapter on sound waves, but I don't see any term defined as acoustic pressure. I am guessing it is the "overpressure", but I don't know of a relationship between overpressure and Intensity.
Have you seen this formula:
[tex] I = { (\Delta P)_{max}^2 \over 2 \rho v} [/tex] ??

Patrick
 
  • #4
No, what is that formula?
 

1. What is acoustic pressure?

Acoustic pressure, also known as sound pressure, is the amount of force per unit area exerted by sound waves. It is measured in units of pascals (Pa) and is a measure of the strength or amplitude of a sound wave.

2. How is acoustic pressure calculated?

Acoustic pressure can be calculated by multiplying the intensity of a sound wave by the square root of the acoustic impedance of the medium through which the sound wave is traveling. The formula is P = √(I * Z), where P is the acoustic pressure, I is the intensity, and Z is the acoustic impedance.

3. What is the relationship between intensity and acoustic pressure?

Intensity and acoustic pressure are directly proportional to each other. This means that as the intensity of a sound wave increases, the acoustic pressure also increases. However, the relationship is not linear and follows a square root function.

4. What is the unit of measurement for acoustic pressure?

The unit of measurement for acoustic pressure is pascals (Pa), which is equivalent to one newton per square meter (N/m²).

5. How can I calculate acoustic pressure for 10 W/m^2 of intensity?

To calculate acoustic pressure for 10 W/m^2 of intensity, you can use the formula P = √(I * Z), where I is the intensity of 10 W/m^2 and Z is the acoustic impedance of the medium. Make sure to use consistent units for intensity and acoustic impedance to get an accurate result.

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