Why are the products of sound wave lengths and frequencies always constant?

In summary, the speed of sound is a constant in a given medium and is determined by the propagation of vibrations from one particle to another. This is due to the linear dispersion relation of sound waves, which results in a constant phase velocity for all frequencies. Unlike other types of waves, the speed of sound is not determined by the frequency and wavelength, but rather by the medium through which it travels.
  • #1
dan1
6
0
Hi everyone!
I was reading a textbook a while ago about waves and it had just finished talking about wave speeds and how it is the product of the frequency times the wave length. On the next page, it gave a table of frequencies and wave lengths of sound waves and how their products are all equal to 340 m/s. I suppose that makes sense: high and low notes at a concert produced at the same time would hit you at the same time. But here's my question: Why is this so? Why is sound always a constant velocity (assuming it is traveling through a consistent medium)?
 
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  • #2
Because the speed of sound is constant in medium.

It's a wave. The frequency is how many times the wave cycles in a second. And the wavelength is the length of a cycle. When you multiply them you get a speed. And the speed will always be the speed of sound.

Frequency = cycles per second. Wavelength = length of a cycle. Multiply them and the answer is in metres per second. It's the speed of the wave.
 
  • #3
For sound traveling through a solid or liquid, particles have electrical bonds with neighboring particles. These bonds are like bouncing springs, with well-defined time delays to return to ther equilibrium position when they have been temporarily deformed. Vibrations move from one particle to the next according to the spring characteristics of the bonds.

For sound traveling through a gas, the particles are independent projectiles that randomly collide with each other, but there is an average probability of such collisions, which depends on the temperature. This governs the transmission of a disturbance along some line.
 
  • #4
A mathematical answer would be that the dispersion relation of the wave equation for sound waves is linear, so the phase velocity is independent of the wave frequency (w/k = c for all w). It's a result of the wave equation.

Not all waves have to be like this- waves on a beach have a more complicated dispersion relation, and they will propagate with different speeds depending on their wavelength.
 
  • #5
dan1 said:
Hi everyone!
I was reading a textbook a while ago about waves and it had just finished talking about wave speeds and how it is the product of the frequency times the wave length. On the next page, it gave a table of frequencies and wave lengths of sound waves and how their products are all equal to 340 m/s. I suppose that makes sense: high and low notes at a concert produced at the same time would hit you at the same time. But here's my question: Why is this so? Why is sound always a constant velocity (assuming it is traveling through a consistent medium)?
As others have indicated, but perhaps useful to emphasize: although the equation could be misinterpreted as such, the wave speed is not the result of the frequency and the wavelength. The source emits a wave with a certain frequency and the medium propagates it at a certain speed. The resulting wavelength is the quotient of the wave speed and the frequency.

See also as introduction:
https://en.wikipedia.org/wiki/Speed_of_sound#Basic_concept
 
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1. Why do different sounds have different wavelengths and frequencies?

Sound waves are created when an object vibrates, causing the air particles around it to also vibrate. The wavelength of a sound wave is determined by the distance between two consecutive peaks or troughs of the wave, while the frequency is determined by the number of vibrations per second. Therefore, different sounds have different wavelengths and frequencies because they are created by different objects vibrating at different rates.

2. How does the wavelength and frequency of a sound wave affect its pitch?

The wavelength and frequency of a sound wave are directly related to its pitch. A higher frequency (shorter wavelength) sound wave will have a higher pitch, while a lower frequency (longer wavelength) sound wave will have a lower pitch. This is because the higher frequency vibrations are interpreted by our ears as a higher pitch sound.

3. Why are the products of sound wavelength and frequency always constant?

The products of sound wavelength and frequency are always constant because the speed of sound in a given medium is constant. This means that as the frequency of a sound wave increases, its wavelength decreases in order to maintain a constant speed. This is known as the inverse relationship between wavelength and frequency.

4. Can the wavelength and frequency of a sound wave change?

Yes, the wavelength and frequency of a sound wave can change. As mentioned earlier, the speed of sound is constant, so if the frequency of a sound wave increases, its wavelength decreases and vice versa. Additionally, the medium through which the sound wave travels can also affect its wavelength and frequency. For example, sound travels at a different speed in water compared to air, resulting in a change in its wavelength and frequency.

5. How do we measure the wavelength and frequency of a sound wave?

The wavelength of a sound wave can be measured by finding the distance between two consecutive peaks or troughs of the wave. The frequency can be measured by counting the number of vibrations or cycles that occur in one second. Both measurements can also be obtained using specialized equipment such as an oscilloscope or a sound level meter.

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