- #1
Fiona Rozario
- 55
- 1
Why does loudness of sound vary as square of amplitude? Why not cube of amplitude or just amplitude?
Why does loudness of sound vary as square of amplitude?
In summary, the loudness of sound is directly related to the amplitude of the sound wave, with an exponential increase in loudness as the amplitude increases. This relationship is consistent for all types of sound waves and can have a significant impact on the perceived loudness of sound. While there may be rare cases where the loudness does not follow this exponential relationship, in most cases the loudness will vary as the square of the amplitude. This relationship also affects the physical properties of sound, such as its intensity and potential for hearing damage.
- #2
Qwertywerty
- 501
- 66
You obtain this result on the mathematical derivation of the intensity.
Edit : This is for the intensity of the sound wave. The loudness(in dB), is measured as β = log(I/I0)dB, where I0 = 10-12W/m2.
You seem to be confused between intensity and loudness
Edit : This is for the intensity of the sound wave. The loudness(in dB), is measured as β = log(I/I0)dB, where I0 = 10-12W/m2.
You seem to be confused between intensity and loudness
Last edited:
- #3
Svein
Science Advisor
- 2,298
- 797
Loudness is a much more complicated thing, as it (usually) refers to what the human ear perceives.
See https://en.wikipedia.org/wiki/Loudness for more information.
See https://en.wikipedia.org/wiki/Loudness for more information.
Related to Why does loudness of sound vary as square of amplitude?
1. Why does loudness of sound vary as square of amplitude?
The loudness of sound is directly related to the amplitude, or height, of the sound wave. As the amplitude increases, the sound wave carries more energy and therefore produces a louder sound. The relationship between loudness and amplitude is not linear, but rather follows an exponential curve. This means that as the amplitude doubles, the loudness increases by a factor of four, or the square of the amplitude.
2. How does the square of amplitude affect the perceived loudness of sound?
The perceived loudness of sound is determined by the intensity of the sound wave, which is directly related to the square of the amplitude. This means that small changes in amplitude can have a significant impact on the perceived loudness of sound. For example, an increase in amplitude from 1 to 2 will result in a perceived loudness increase of 4.
3. Is the relationship between loudness and amplitude consistent for all types of sound waves?
Yes, the relationship between loudness and amplitude is consistent for all types of sound waves, including both mechanical and electromagnetic waves. This is because the loudness of sound is determined by the amount of energy carried by the sound wave, which is directly proportional to the square of the amplitude.
4. Can the loudness of sound ever vary in a non-exponential manner?
In rare cases, the loudness of sound may not follow an exponential relationship with the amplitude. This can occur when the sound source is very close to the listener, or when the sound is distorted or muffled in some way. However, in most cases, the loudness of sound will vary as the square of the amplitude.
5. How does the square of amplitude affect the physical properties of sound?
The square of the amplitude affects the physical properties of sound by determining the intensity, or energy, of the sound wave. This can impact factors such as the distance the sound can travel, the amount of sound energy absorbed by different materials, and the potential for hearing damage at high amplitudes. Understanding the relationship between loudness and amplitude is important for accurately measuring and controlling sound levels in various settings.
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