# Speed of sound versus frequency

• pixel01
In summary, the speed of sound does not depend on its frequency, but rather on the elastic/inertial properties of the medium and the wavelength. This can be seen in a practical example with an orchestra, where varying speeds would result in a lack of musical harmony. However, in some cases, the speed of sound can vary with frequency if the medium does not respond adiabatically. This is determined by the adiabatic process and the value of \gamma, which for diatomic gasses is 5/2. In the case of air, which behaves closely to an ideal gas, the measured speed of sound aligns with the theoretical prediction due to the adiabatic process.

#### pixel01

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

pixel01 said:
My question is : does the speed of sound depend on its frequency?
All other medium conditions considered identical.
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

tonyh said:
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

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

pixel01 said:
I always thought like that, but this is what I copied from wiki:
"The medium in which a sound wave is traveling does not always respond adiabatically, and as a result the speed of sound can vary with frequency".
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.

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.

## 1. What is the relationship between the speed of sound and frequency?

The speed of sound and frequency are inversely proportional. This means that as frequency increases, the speed of sound also increases. However, the rate of change is not constant and varies depending on the medium through which sound travels.

## 2. How does the speed of sound change with different frequencies?

The speed of sound increases as the frequency increases. This is because higher frequency sound waves have shorter wavelengths, which allows them to travel through a medium more quickly. In general, the speed of sound in air increases by about 0.6 meters per second for every degree increase in temperature.

## 3. What is the significance of the speed of sound versus frequency?

The speed of sound versus frequency relationship is important in understanding how sound travels through different mediums. It also plays a role in the quality of sound produced by musical instruments and in the design of acoustic spaces. Additionally, it has practical applications in fields such as seismology and ultrasound technology.

## 4. How is the speed of sound at a specific frequency calculated?

The speed of sound at a specific frequency can be calculated using the formula v = fλ, where v is the speed of sound, f is the frequency, and λ is the wavelength. This formula is based on the relationship between frequency, wavelength, and the speed of sound in a given medium.

## 5. Does the speed of sound change with different types of sound waves?

Yes, the speed of sound can vary depending on the type of sound wave. For example, in air, the speed of sound is faster for longitudinal waves (such as sound waves) compared to transverse waves (such as light waves). Additionally, the speed of sound can also be affected by factors such as temperature, humidity, and altitude.