# Speed of sound versus frequency

1. Jun 5, 2008

### pixel01

My question is : does the speed of sound depend on its frequency?
All other medium conditions considered identical.

2. Jun 5, 2008

### tonyh

No. The frequency is set by the oscillating body which sets up the sound waves. The speed of the waves is determined by the elastic/inertial properties of medium and the wavelength is then given by $$\lambda$$= v/f.
As a practical example, think about an orchestra. If v did vary with f, the sounds from the different instruments would reach your ears at different times. The result would not be very musical

3. Jun 5, 2008

### pixel01

I always thought like that, but this is what I copied from wiki:
"The medium in which a sound wave is travelling does not always respond adiabatically, and as a result the speed of sound can vary with frequency".

4. Jun 5, 2008

### tonyh

Possibly? An adiabatic process is one that occurs so rapidly, or in a system so well insulated, such that we can consider the heat transfer (Q) to be zero. But I do not know enough about the subject to be able to judge the wiki quote. My answer applies to a simple models though- at the very least, it's a good rule of thumb.

5. Jun 5, 2008

### rbj

air at room temperature is so close to an ideal gas that the compressions and rarefractions of sound through reasonably dry air would be nearly completely adiabatic. if it is completely adiabatic, then

$$P v^\gamma = \mathrm{constant}$$

and for diatomic gasses (air is 21% O2 and 78% N2) then $\gamma = 5/2$. the speed of sound is dependent on that $\gamma$ and the measured speed of sound in air comes out very close to what the theory predicts. if the process weren't adiabatic, then there would not be the close agreement between the theory and experimental result.