Speed of Sound & Density/Temp Relationship

Click For Summary
SUMMARY

The speed of sound in a medium is determined by the elasticity and density of that medium, expressed by the equation s = √(E/D), where E is Young's modulus and D is density. For air, Young's modulus can be approximated as E = 1.41P, indicating that pressure does not affect the speed of sound. The relationship between temperature and density shows that sound speed varies with the square root of temperature, leading to the formula S1/S2 = √(T1/T2). For example, sound travels at 741 mph at 0°C (273 K) and increases to approximately 770 mph at room temperature (22°C or 295 K).

PREREQUISITES
  • Understanding of Young's modulus in materials science
  • Knowledge of the ideal gas law and its implications on density
  • Familiarity with temperature scales, specifically Kelvin
  • Basic principles of wave propagation in gases
NEXT STEPS
  • Research the relationship between temperature and sound speed in different gases
  • Explore the effects of humidity on the speed of sound in air
  • Study the impact of altitude on air density and sound propagation
  • Learn about acoustic properties of various materials beyond air
USEFUL FOR

Physicists, acoustics engineers, meteorologists, and anyone interested in the principles of sound propagation in different mediums.

Quasaire
Messages
16
Reaction score
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).
 
Physics news on Phys.org
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.
 
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.
 

Similar threads

Undergrad Why Can a Sound Wave Not Travel Faster than the Average Molecule Speed?
  • · Replies 23 ·
Replies
23
Views
4K
Undergrad A Question About Shock Waves From an Airplane
  • · Replies 82 ·
3
Replies
82
Views
8K
Undergrad How fast does a blastwave travel?
  • · Replies 236 ·
8
Replies
236
Views
18K
Undergrad Why is there a set speed of sound in a certain medium?
  • · Replies 7 ·
Replies
7
Views
2K
Graduate Speed of sound: viscosity dependece in liquids and solids
  • · Replies 12 ·
Replies
12
Views
3K
High School What sound frequencies can pass through a hole in a wall?
  • · Replies 31 ·
2
Replies
31
Views
5K
Graduate Maths for Sound passing through different mediums
  • · Replies 10 ·
Replies
10
Views
3K
Graduate Confusion about the derivation of the speed of sound
  • · Replies 8 ·
Replies
8
Views
3K
Undergrad The Speed of Sound: Changing with Medium
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad How does density affect the speed of sound?
  • · Replies 1 ·
Replies
1
Views
4K