# Relation between sound intensity and frequency

• Tulio Cesar
In summary, the sound intensity formula is dE/dT*dS, with variables including energy, area, and time. The relationship between frequency and sound intensity is often not mentioned, but time is an important factor in determining how long it takes for the energy of a wave to pass through an area. This means that two notes with the same amplitude can have different sound intensities depending on their frequency. However, the intensity of a sound also depends on how the wave is described, either by particle displacement or pressure amplitude. When talking about hearing a sound, the sensitivity of the ear to different frequencies can also affect the perceived loudness.
Tulio Cesar
The sound intensity formula is given by: dE/dT*dS. So the variables are energy, related to the amplitude of the wave, area, related to wavefronts distribution on space, and time. So many times I don't see any reference about the relation between frequency and sound intensity, but if time is a variable, so shouldn't it be important to know how much time the energy of a wave does take to pass through an area? If so, is it correct to assert that the G note, having the same amplitude (and consequently being as loud) of A note, has therefore more sound intensity?
Please correct any conceptual mistake i may have done and elucidate the topic for me.

It depends on ow do you define the amplitude. If you describe the wave by particle displacement then indeed the intensity depends on frequency.
However, more common is to use pressure amplitude and in this case the intensity does not depend on frequency.

If you are talking about hearing a sound, then the sensitivity of the ear depends on frequency and sounds with the same intensity but different frequencies may be perceived as having different loudness levels.

## 1. What is sound intensity?

Sound intensity refers to the amount of energy carried by sound waves per unit area. It is measured in watts per square meter (W/m^2).

## 2. How is sound intensity related to frequency?

Sound intensity and frequency are directly proportional to each other. This means that as the frequency of a sound increases, the intensity also increases.

## 3. What is the decibel scale and how is it related to sound intensity and frequency?

The decibel scale is a logarithmic scale used to measure the intensity of sound. It is directly related to sound intensity and frequency, as an increase in sound intensity of 10 times results in an increase of 10 decibels, and an increase in frequency also results in an increase in decibels.

## 4. How does sound intensity affect the human ear?

The human ear has a range of sensitivity to sound intensity, meaning that extremely low or high intensity sounds may not be audible. Prolonged exposure to high intensity sounds can also damage the delicate structures in the ear, leading to hearing loss.

## 5. Can sound intensity and frequency be manipulated for different purposes?

Yes, sound intensity and frequency are important factors in many applications, such as music production, noise cancellation, and medical treatments. They can be manipulated to achieve desired effects, such as creating a specific sound or reducing unwanted noise.

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