A Question about Loudness of Sound....

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Discussion Overview

The discussion revolves around the concept of loudness of sound, specifically exploring how the area of a vibrating body affects the loudness when the amplitude of vibration remains unchanged. Participants examine the relationship between energy transfer, area, and perceived loudness, touching on both theoretical and practical aspects of sound propagation.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants assert that increasing the area of a vibrating body increases loudness, while maintaining amplitude results in the same energy per unit area impacting the eardrum.
  • One participant challenges the assumption that energy per unit area remains constant, suggesting that a larger source surface allows for multiple paths to the eardrum, potentially increasing the overall energy received.
  • Another participant distinguishes between listening distances, noting that increasing speaker area has different effects depending on proximity to the sound source.
  • A participant argues that a small vibrating object cannot effectively couple energy into the air compared to a larger one, and that larger speaker cones require less movement to achieve the same acoustic power.
  • Discussion includes the concept of radiation zones, explaining how sound propagation differs in near and far zones, affecting intensity and directivity.
  • Concerns are raised about the efficiency of sound radiation when the diaphragm dimensions are smaller than the wavelength, leading to cancellation of sound waves and reduced coupling to the medium.

Areas of Agreement / Disagreement

Participants express differing views on the relationship between area, amplitude, and loudness, with no consensus reached on how these factors interact in terms of energy transfer and perceived sound intensity.

Contextual Notes

Some assumptions about energy transfer and sound propagation remain unresolved, particularly regarding the effects of distance and the mechanics of sound coupling in different scenarios.

Kaneki123
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OKay...Loudness of a sound is "the magnitude of sensation of human ear", or ''how much violently ear drum vibrates due to sound wave" (That is according to my understanding)...Now, increasing the area of vibrating body increases the loudness of sound...My question is that, if we increase area of vibrating body without changing its amplitude of vibration, then the energy per unit area will be the same, meaning the energy vibrating per unit of ear drum will be the same, meaning it will vibrate with same amplitude as before. So how can the loudness of such sound be increased?...Any help will be appreciated...
 
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Kaneki123 said:
My question is that, if we increase area of vibrating body without changing its amplitude of vibration, then the energy per unit area will be the same

True.

meaning the energy vibrating per unit of ear drum will be the same,

Why would you think that? Keep in mind that with a bigger source surface, there are many more paths from the source to a given spot on the eardrum. Those all add up.
 
Kaneki123 said:
OKay...Loudness of a sound is "the magnitude of sensation of human ear", or ''how much violently ear drum vibrates due to sound wave" (That is according to my understanding)...Now, increasing the area of vibrating body increases the loudness of sound...My question is that, if we increase area of vibrating body without changing its amplitude of vibration, then the energy per unit area will be the same, meaning the energy vibrating per unit of ear drum will be the same, meaning it will vibrate with same amplitude as before. So how can the loudness of such sound be increased?...Any help will be appreciated...
It seems to me that you are conflating two scenarios.

If you are listening to a sound at a large distance from some small speakers, increasing the speaker area will increase the sound amplitude where you ear is located.

If you are listening to a sound at a small distance from some large speakers, increasing the speaker area does little or nothing. The amplitude at your ears is equal to the amplitude at the source.

If you want to increase the amplitude at your ear above that put out by the speakers, you could try a parabolic reflector.
 
Kaneki123 said:
if we increase area of vibrating body without changing its amplitude of vibration, then the energy per unit area will be the same,
That's not true, actually because a small vibrating object just can't couple much energy into the air. A small loudspeaker cone will have to move much further than a large speaker cone, to set up the same Acoustic Power. This is why we use soundboards and other sorts of resonators if we want to make a musical instrument loud enough.
I may get complaints that that's too simple an argument but it is appropriate, I think, and covers most situations.
Launching and receiving sound waves is all about 'Matching Impedances' to maximise the transfer of energy at an interface. The well known Ossicles in the ear act as levers to match the impedance of air to the impedance of the fluid in the inner ear. (They do not 'amplify' the sound, as you will read in countless elementary articles about sounding hearing. Amplifiers need a power supply and the three bones have none.))
 
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Kaneki123 said:
OKay...Loudness of a sound is "the magnitude of sensation of human ear", or ''how much violently ear drum vibrates due to sound wave" (That is according to my understanding)...Now, increasing the area of vibrating body increases the loudness of sound...My question is that, if we increase area of vibrating body without changing its amplitude of vibration, then the energy per unit area will be the same, meaning the energy vibrating per unit of ear drum will be the same, meaning it will vibrate with same amplitude as before. So how can the loudness of such sound be increased?...Any help will be appreciated...
When we are close to a radiating aperture, which for the case of sound might be a vibrating diaphragm, we are in a Radiation Near Zone, also called the Fresnel Region. The shape of the radiated field is different to that at a large distance from the aperture, which is known as the Radiation Far Zone or Fraunhofer Region.
In the RFZ the diaphragm radiates a narrow beam with a number of weaker side lobes. In the RNZ it radiates essentially a parallel beam with blobs of energy dotted around. So a large diaphragm has increased directivity at great distances, increasing the received intensity, but reduces the intensity close up, because the energy is spread over a greater area.
In addition to this, if the dimensions of the diaphragm are smaller than about a wavelength, then, as mentioned by Sophie Centaur, the radiating efficiency is low. Sound waves from the front of the diaphragm are canceled by those from the back, and the diaphragm does not couple very well to the medium. This is because sound waves from the front of the diaphragm are canceled by those from the back. We say that the mechanical radiation resistance of the diaphragm has become small.
 

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