Calculating Speed of Sound in Air at 30 Degrees with Young and Bulk Modulus"

[noobie!]

Speed of sound at...

Homework Statement

find the values of the speed of sound in air at 30 degree.. Young modulus of cu=11 X 10^10 N/m^2 ,Bulk modulus of water=2.2 X 10^9 N/m^2 , density,p of copper=8.9 X 10^3 Kg/m^3 , density of water=1.0 X 10^3 kg/m^3

Homework Equations

do not have..sorry

The Attempt at a Solution

using formula of sound waves in gases v= square root of gamma . RT/M (ideal gas) but I am stuck with M?

 

[anathema]

Thank you for your question. The speed of sound in air at 30 degrees can be calculated using the formula v = √(γRT/M), where v is the speed of sound, γ is the adiabatic index (1.4 for air), R is the gas constant (8.314 J/mol•K), T is the temperature in Kelvin (30 + 273 = 303 K), and M is the molar mass of air.

To find the molar mass of air, we can use the ideal gas law, PV = nRT, where P is the pressure (atmospheric pressure at sea level is approximately 1.01325 x 10^5 Pa), V is the volume (can be assumed to be 1 m^3 for simplicity), n is the number of moles (unknown), and R is the gas constant as stated above. Rearranging this equation to solve for n gives us n = PV/RT. Plugging in the values from above and using the molar volume of an ideal gas (22.4 L/mol), we get n = (1.01325 x 10^5 Pa)(1 m^3)/(8.314 J/mol•K)(303 K) = 41.8 moles.

Now we can use the molar mass of air, which is approximately 29 g/mol, to calculate the speed of sound in air at 30 degrees:

v = √(1.4)(8.314 J/mol•K)(303 K)/(41.8 moles)(0.029 kg/mol) = 344.4 m/s

I hope this helps you with your calculations. Let me know if you have any further questions.

 

[thomate1]

Dear student,

Thank you for your question. Your attempt at solving the problem using the ideal gas law is a good start. However, since we are dealing with the speed of sound in air, we need to use the properties of air instead of an ideal gas.

To calculate the speed of sound in air at 30 degrees, we can use the following formula:

v = √(γRT/M)

Where:
v = speed of sound in air
γ = adiabatic index for air (1.4)
R = gas constant for air (287 J/kg K)
T = temperature in Kelvin (30 degrees = 303 K)
M = molar mass of air (28.97 g/mol)

To find the molar mass of air, we can use the following formula:

M = (m1/M1) + (m2/M2) + ... + (mn/Mn)

Where:
m = mass of each component (in this case, nitrogen and oxygen)
M = molar mass of each component (for nitrogen, M = 28 g/mol; for oxygen, M = 32 g/mol)

Using the given densities for copper and water, we can find the mass of each component in air. The mass of nitrogen is (1-0.089) * 1.0 * 8.9 = 0.801 g, and the mass of oxygen is (0.089) * 1.0 * 1.0 = 0.089 g. Plugging these values into the molar mass formula, we get:

M = (0.801/28) + (0.089/32) = 0.0286 + 0.0028 = 0.0314 g/mol

Now, we can plug all of these values into the speed of sound formula:

v = √(1.4 * 287 * 303 / 0.0314) = 347 m/s

Therefore, the speed of sound in air at 30 degrees is approximately 347 m/s. I hope this helps you with your homework. Good luck!