# I Why is there a set speed of sound in a certain medium?

Tags:
1. Dec 10, 2016

### Surya97

• Why does sound always move at the local speed of sound in a medium (in other words, why is there a set speed of sound for certain medium)? I understand that sound is a compression wave, but shouldn't a louder sound (i.e. one with a higher amplitude) move faster? What about a higher pitch noise (i.e. one with a higher frequency)?
• Is there a way to create shock waves without moving something through a medium at greater than the local speed of sound?
• Is the speed of sound the limit of a mechanical waves propagation speed?
Thanks in advance for the answers!

2. Dec 10, 2016

### Charles Kottler

The speed of sound is governed by the elastic properties and density of a substance. For a simple description see:
https://www.nde-ed.org/EducationResources/HighSchool/Sound/speedinmaterials.htm

Surface waves (gravity waves) are not quite the same as sound waves but the principle is similar. Imagine pushing an object through water near the surface: at any speed less than the wave speed the leading edge of the wave will recede faster than the source. As the first peak recedes from the source the momentum of the falling water causes a trough to form, so you end up with a series of waves propagating away from the source. An increase in the speed of the object will cause the height to increase but because the leading edge is receding faster the free movement of the water controls the wave shape rather than the source of the wave.
Once the speed of the source matches the wave speed the dynamics change - in the case of a surface wave the face becomes turbulent.

A sound is generated by an oscillating object. As long as the maximum speed of the source remains lower than the speed of sound I would expect the waves to form nicely. The speed is a function of the amplitude and frequency so there will be a point at which either an increase in amplitude or in pitch will cause the source of the sound to move faster than the speed of sound. In the case of excessive amplitude the wave shape will be distorted but the frequency (pitch) will remain the same so the sound quality will drop. With excessive frequency I imagine you will get changing levels of wave distortion as the propagated waves come in and out of phase with the source.

When a wave moves faster than the local speed pf sound in a fluid it is a shock wave (Wikipedia). The speed of a shockwave will decrease as it dissipates until it just becomes a sound wave.

I am getting way beyond my level of knowledge here, but I guess if you had two or more sources of sound of sufficient amplitude or frequency then the conditions where the waves meet could form a shockwave. A sound moving from one medium to another might also do this.

3. Dec 10, 2016

### davenn

The speed and frequency of sound are independent of amplitude

4. Dec 10, 2016

### mfig

The speed at which a wave moves through a material is a function of the properties of the material. So it makes sense that if the properties are set, which they are for any given material at given conditions, then the speed of a wave through that material is fixed.
It depends on how particular you are with what you mean by "moving something" through the medium. An expansion wave can be induced in an absorbent gas by passing a powerful laser through it. This can also be accomplished by discharging a high voltage spark through a gas.
See detonation waves.

5. Dec 10, 2016

### Surya97

When the oscillating object increases or decreases in speed, why does the speed of the sound generated stay the same (as long as the object is moving at subsonic speeds)?

6. Dec 10, 2016

### mfig

The speed of a sound wave through a material depends on the properties of the material, and not the particulars of the disturbance which gives rise to the wave.

7. Dec 10, 2016

### Staff: Mentor

Once a wave peak has moved away from the source and is propagating through the medium, its speed is going to be determined by the characteristics of the medium because the source is no longer there to influence it. Thus, the motion of the source will influence the spacing between wave peaks - if the source is moving left while the wave is moving right, each new peak will be started farther left from the previous peak than if the source were at rest (google for "Doppler effect") - but not the speed of the peaks.

You marked this thread as I-level, so you'll be able to handle elementary differential equations. Google for "wave equation"; this is the differential equation that relates the speed of waves in a medium to the stiffness and density of the medium. Solve it, and you'll see a firm mathematical statement of the hand-waving "once a wave peak has moved away from the source..." statement that I made in the previous paragraph.

8. Dec 12, 2016

### Charles Kottler

If you are talking about sound in a gas, temperature is the main variable factor affecting the speed. With 'normal' sounds the pressure difference is small enough that temperature changes are negligible. A higher frequency can cause a slight increase in speed:

https://en.wikipedia.org/wiki/Speed_of_sound#Effect_of_frequency_and_gas_composition
"The dependence on frequency and pressure are normally insignificant in practical applications. In dry air, the speed of sound increases by about 0.1 m/s as the frequency rises from 10 Hz to 100 Hz. For audible frequencies above 100 Hz it is relatively constant. Standard values of the speed of sound are quoted in the limit of low frequencies, where the wavelength is large compared to the mean free path."

Large amplitude low frequency sounds cause easily measurable movement (wind): see http://physicsworld.com/cws/article/news/2015/apr/02/dousing-flames-with-low-frequency-sound-waves - a higher frequency wave moving through this will presumably be distorted.

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted