Pressure Amplitude and Decreasing Intensity

In summary, when a point source emits sound, the sound travels away from the source as a series of spherical wavefronts. The energy of the wave is conserved, but as it spreads out over the spherical surface area, the intensity and pressure amplitude of the wave decrease according to an inverse square law. This explains why the pressure amplitude of a wave should decrease as it moves away from the source. However, for a single longitudinal wave, the intensity and pressure amplitude should remain constant. This apparent paradox can be resolved by considering the spherical wavefront explanation, which shows that amplitude must decrease as we move farther away from the source. This is due to the fact that the intensity of a wave decreases as it spreads out over a larger surface area
  • #1
modulus
127
3
When a point source emits sound, the sound travels away from the source as a series of wavefronts - all being spherical shells - away from the source right?

Now, we say the energy is conserved if we neglect damping forces in the medium, and so the power delivered by the source should be equal to the power delivered by a single wavefront at a certain distance from the source.

Power equals the intensity at a wavefront times the area of that wavefront. And, the intensity from a particular sound wave is proportional to the square of the pressure amplitude of the wave.

So, when a sound wave reaches a particular distance from the source, the pressure amplitude of the wave should decrease, as, at that distance, it is part of a wavefront, whose sound intesity is less than that of another wavefront closer to the source.

But, we also consider energy to be conserved for a single wave. But this is not possible, if we proceed by the above logic that explains why the pressure amplitude of a wave should decrease as it moves away from the source...?

This apparent paradox is going to make me mad...someone help, please!
 
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  • #2
You could write out some equations so we could see why you think energy is not conserved.
 
  • #3
"To a good first approximation, wave energy is conserved as it propagates through the air. In a spherical pressure wave of radius , the energy of the wavefront is spread out over the spherical surface area . Therefore, the energy per unit area of an expanding spherical pressure wave decreases as . This is called spherical spreading loss. It is also an example of an inverse square law which is found repeatedly in the physics of conserved quantities in three-dimensional space. Since energy is proportional to amplitude squared, an inverse square law for energy translates to a decay law for amplitude."

https://ccrma.stanford.edu/~jos/pasp/Spherical_Waves_Point_Source.html
 
  • #4
"To a good first approximation, wave energy is conserved as it propagates through the air. In a spherical pressure wave of radius , the energy of the wavefront is spread out over the spherical surface area . Therefore, the energy per unit area of an expanding spherical pressure wave decreases as . This is called spherical spreading loss. It is also an example of an inverse square law which is found repeatedly in the physics of conserved quantities in three-dimensional space. Since energy is proportional to amplitude squared, an inverse square law for energy translates to a decay law for amplitude."

Okay, so that explains exactly why amplitude should decrease as we move away from the source...it's according to the concept that the energy is spread out across the wavefront.

But, how does that translate in terms of linear sound waves? Pressure amplitude can't decrease as we move along a single longitudinal sound wave ,because energy is conserved along that single wave too.

?
 
  • #5
Okay, about formulas:

The formula for the intensity (which is the power delivered by a wave per unit area) of a wave at any point on it (assuming all points along the wave have the same amplitude, frequency, etc.) is:

Intensity = 0.5 * (Density Of The Medium) * (Speed of Sound in the Medium) * (Angular Frequency of a Particle Oscillating on the Wave) * (Displacement Amplitude of a Particle Oscillating on the Wave)

For a single wave, none of these parameters changes along a wave.
But, considering the spherical wavefront explanation, the intensity decreases as we move farther away from the source (along a wave away from the source), and that demands that the amplitude decrease, as all the other parameters will remain constant for the single longitudinal wave - a point of which will constitute the wavefront at a certain distance from the source)...
 

1. What is pressure amplitude and how is it measured?

Pressure amplitude refers to the maximum deviation from the average pressure in a sound wave. It is typically measured in units of Pascals (Pa) using a microphone or other pressure-sensing device.

2. How does decreasing intensity affect pressure amplitude?

Decreasing intensity results in a decrease in pressure amplitude. This is because intensity is directly proportional to pressure amplitude, meaning that as intensity decreases, so does pressure amplitude.

3. What is the relationship between pressure amplitude and sound volume?

The relationship between pressure amplitude and sound volume is direct. As pressure amplitude increases, so does sound volume. This is because higher pressure amplitudes result in more energy being transferred to the medium, resulting in a louder sound.

4. Can pressure amplitude be used to measure the loudness of a sound?

Yes, pressure amplitude can be used to measure the loudness of a sound. This is because, as mentioned before, pressure amplitude and sound volume are directly related. However, other factors such as frequency and distance from the sound source also play a role in determining loudness.

5. How does pressure amplitude affect the quality of sound?

Pressure amplitude does not directly affect the quality of sound. Quality is determined by factors such as frequency, harmonics, and timbre. However, pressure amplitude can indirectly affect quality by influencing sound volume, which can impact the perception of sound quality.

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