Is the Density of Gas Always 1.29 kg/m³ in Harmonic Sound Wave Calculations?

[cseet]

Hi all,

can somebody advise on this,

Equation:
P (change in pressure) = p (density of gas)*w*v*s(max displacement amplitute)

P = pwvs

Needed to know, is the density of gas always at 1.29kg/m(3)?

I've this following qeustion:
A piston at one end of a long tube filled with air at room temperature and normal pressure oscillates with a frquency at 500Hz and an amplitude of 0.1mm. What is the intensity of the waves?

answer:
P=pwvs
= 1.29*2pie(500)*340*1E-4
= 138Pa

if the density of gas does not always = 1.29kg/m(3), then how can I calculate the density of gas from the above question?

thanks
cseet

 

[lippyka]

In this case, the density of gas is assumed to be constant and equal to 1.29kg/m3. If the density of the gas changes with temperature, pressure, or other factors, then you would need to use the appropriate equation to calculate the density from the given conditions. However, in the case of the question you have provided, assuming a constant density of 1.29kg/m3 is valid.

 

[M98Ranger]

Hi cseet,

Thank you for your question. The equation you have provided is the equation for a harmonic sound wave, where P is the change in pressure, p is the density of gas, w is the angular frequency, v is the velocity of sound, and s is the maximum displacement amplitude.

To answer your question, the density of gas is not always 1.29 kg/m³. This value is for air at room temperature and normal pressure, which is commonly used as a standard for calculations. However, if the conditions are different, then the density of gas will also be different. In order to calculate the density of gas, you would need to know the temperature, pressure, and type of gas in the tube. Then, you can use the ideal gas law to calculate the density.

In the given question, the intensity of the waves can be calculated using the equation I = P/A, where I is the intensity, P is the pressure, and A is the cross-sectional area of the tube. Since the piston is oscillating, the intensity will also be oscillating. To find the maximum intensity, you can use the equation I(max) = P(max)/A.

I hope this helps answer your question. Let me know if you need any further clarification. Best of luck with your studies!