Principle Determining the Loudness (Intensity) of Sound

In summary, the loudness of sound is determined by energy, which is conserved but spreads out in a sphere. This means that at 3 times the distance from the source, the same amount of energy is spread out over 9 times the area, resulting in a decrease in loudness. This can be seen in the analogy of a stone's ripples in a pool of water, where the amplitude decreases with distance. This is also true for other types of waves, such as tsunamis. The energy in a wave is determined by both its amplitude and the surface area it covers.
  • #1
Impulse
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A test question I was asked earlier in the year has been hanging around in the back of my mind:

"If a radio is moved 3x further away from you, how is its loudness affected?"

To answer this question one needs to know what determines the loudness of sound. What determines the loudness of sound?

Is the loudness of sound determined solely by the amplitude of the sound wave? I answered based on this reasoning, and said that the radio would be equally loud 3x further away because its sound waves would have equal amplitude at distances x and 3x.
 
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  • #2
Impulse said:
A test question I was asked earlier in the year has been hanging around in the back of my mind:

"If a radio is moved 3x further away from you, how is its loudness affected?"

To answer this question one needs to know what determines the loudness of sound. What determines the loudness of sound?

Is the loudness of sound determined solely by the amplitude of the sound wave? I answered based on this reasoning, and said that the radio would be equally loud 3x further away because its sound waves would have equal amplitude at distances x and 3x.
The "loudness" ("amplitude") depends on energy. Energy is conserved but the sound wave spreads out in a sphere. So at 3 times the distance the same amount of energy is spread out over 9 times the area.

(Do you really believe that a radio sounds just as loud no matter how far away you are?)
 
  • #3
Loudness is determined by energy. Got it. Based on that, it makes intuitive sense that the further away one is from the source, the less energy one will receive (i.e. heat energy from the sun decreases with distance).

Still, I don't fully understand how the energy is spreading out into space. When I imagine a wave, I think of a two-dimensional structure like a sine wave or the longitudinal wave animation here: http://www.acs.psu.edu/drussell/demos/waves/wavemotion.html

In the above animation, because the longitudinal wave is in a rectangular pool and generated from a wall of the pool, and not a point source, the amplitude and energy are constant irrespective of distance travelled.

If I imagine light (or sound) as particles, it is easy to picture the energy spreading out into a sphere. I don't see that picture with waves, because I picture a constant amplitude and don't see it diminishing with distance (i.e. I don't image a graph of sine with decaying amplitude).

Intuitively I don't think it's crazy for a radio to be just as loud 3x further away. Isn't a laser just as intense 3x further away from its source?

Also, if energy travels outward like a sphere, why is the relationship not inverse cube with distance? The formula for volume of a sphere = (4/3)pi(r^3).

How do you picture the propagation and energy distribution of sound waves? Do you picture waves, or particles / packets of energy?
 
  • #4
Impulse said:
When I imagine a wave, If I imagine light (or sound) as particles, it is easy to picture the energy spreading out into a sphere. I don't see that picture with waves, because I picture a constant amplitude and don't see it diminishing with distance (i.e. I don't image a graph of sine with decaying amplitude).

The amplitude of a spherical wave does indeed decrease with distance from the center. For a two-dimensional analog, have you ever dropped a stone into a pool of water and watched the circular ripples expand? Their amplitude also decreases.

Isn't a laser just as intense 3x further away from its source?

A laser beam does expand gradually with distance, but the description is more complicated than with a simple point source.

Also, if energy travels outward like a sphere, why is the relationship not inverse cube with distance? The formula for volume of a sphere = (4/3)pi(r^3).

What matters is the surface area of the sphere (4πr2), not its volume. Your ears intercept part of this surface area as it reaches your location a distance r from the source.
 
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  • #5
jtbell said:
The amplitude of a spherical wave does indeed decrease with distance from the center. For a two-dimensional analog, have you ever dropped a stone into a pool of water and watched the circular ripples expand? Their amplitude also decreases.

I was imagining that as I wrote my reply. Is there a way to calculate the rate at which the amplitudes decrease?

I read that tsunamis undergo little energy loss with distance travelled. Are they not a point-source wave? Also, the amplitude of waves increases as it nears the shore, "shoaling", yet its total energy couldn't be increasing. Is there more to energy of a wave than just amplitude?

In general, what determines the energy in a wave?

jtbell said:
A laser beam does expand gradually with distance, but the description is more complicated than with a simple point source.

Okay, cool.

jtbell said:
What matters is the surface area of the sphere (4πr2), not its volume. Your ears intercept part of this surface area as it reaches your location a distance r from the source.

Makes sense. The energy doesn't fill the entire space at once (volume) but expands out through it (surface area). Thanks.
 

FAQ: Principle Determining the Loudness (Intensity) of Sound

1. How is the loudness of sound measured?

The loudness of sound is measured in decibels (dB), which is a logarithmic unit that compares the intensity of a sound to a reference level. The reference level is typically the lowest sound that a human ear can detect, which is equivalent to 0 dB.

2. What factors affect the loudness of sound?

The loudness of sound can be affected by several factors, including the distance from the source of the sound, the amplitude or intensity of the sound waves, and the frequency or pitch of the sound. Additionally, the environment in which the sound is produced and received can also impact its loudness.

3. How does the human ear perceive loudness?

The human ear perceives loudness based on the intensity of sound waves, which is measured in decibels. However, the human ear is not equally sensitive to all frequencies, and higher frequencies require greater intensity to be perceived as equally loud as lower frequencies.

4. Can sound be too loud?

Yes, sound can be too loud and can potentially cause damage to the ears. Prolonged exposure to sounds above 85 dB can lead to hearing loss. It is important to protect your ears by wearing earplugs or reducing exposure to loud noises when possible.

5. How does the loudness of sound affect its impact on humans?

The loudness of sound can have a significant impact on humans, both physically and psychologically. Exposure to loud noises can cause physical discomfort and even pain, as well as contribute to stress and anxiety. On the other hand, soft or soothing sounds can have a calming effect on the body and mind.

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