Speed of Sound & Density/Temp Relationship

In summary, the speed of sound in a medium is determined by its density and temperature. This can be expressed by the equation s= [squ](E/D), where E is the elasticity (Young's modulus) and D is the density. For air, the elasticity is approximately 1.41 times the barometric pressure, and density varies inversely with temperature (in Kelvin). Therefore, the speed of sound in air at room temperature (22°C or 295°K) is approximately 770 mph, compared to 741 mph at 0°C (273°K). Barometric pressure does not significantly affect the speed of sound, as it only affects the density of the medium.
  • #1
Quasaire
16
0
Does anyone have an equation that gives the speed of sound in respect to the density and temperature of the medium in which the sound wave is propagating? I know the speed of sound in average temperature air molecules is like 700mph (I think).
 
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  • #2
The speed of sound is equal to

s= [squ](E/D)

where E is the elasticity(Young's modulus) and D is the density.

For air, E = 1.41P (approx.)

Since pressure and density go hand in hand, barometric pressure does not effect the speed of sound.

Density varies inversely by temp(Kelvin), so the speed of sound varies by the squareroot of temp.

thus : S1/S2 = [squ](T1/T2)

Sound travels through air at 332 m/s (741mph) at 0°C (273°K) so at room temp 22°C (295°K), it would travel at

S2 = 741/[squ](273/295) = 770 mph

Etc.
 
  • #3
Originally posted by Janus
Since pressure and density go hand in hand, barometric pressure does not effect the speed of sound.
This one always confused me, so let me expand. Hell, my understanding may even be wrong, but it makes sense to me :wink:. Sound waves propagate by air molecules bouncing off of each other. Since the speed an air molecule travels is determined by temperature (and its mass of course), that's what determines the speed of sound. In air less dense, each individual molecule will travel further than in more dense air, but the speed it travels before hitting the next molecule is unchanged.
 

1. How does the speed of sound change with temperature?

The speed of sound increases with an increase in temperature. This is because sound travels faster through materials with higher molecular speeds, which is the case with warmer temperatures. For every 1 degree Celsius increase in temperature, the speed of sound increases by 0.6 meters per second.

2. What is the relationship between density and the speed of sound?

The speed of sound is directly proportional to the square root of the medium's density. This means that as the density of a material increases, the speed of sound also increases. This relationship is known as the density/temperature relationship.

3. How does the speed of sound change with altitude?

The speed of sound decreases with an increase in altitude. This is because the air becomes less dense at higher altitudes, causing sound waves to travel slower. This is why sound appears to be muffled at high altitudes.

4. Does the speed of sound vary with different materials?

Yes, the speed of sound varies with different materials. It is dependent on the density, elasticity, and temperature of the material. For example, sound travels faster in solids than in liquids or gases because the particles are closer together and can transmit sound waves more efficiently.

5. How is the speed of sound measured?

The speed of sound can be measured using a variety of methods, such as using an oscilloscope and a microphone to measure the time it takes for a sound wave to travel a known distance. It can also be calculated by knowing the temperature and density of the medium using mathematical equations such as the Newton-Laplace formula or the ideal gas law.

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