Microphone Diaphragm size and Proximity Effect

[deb611]

Been reading a lot about the physics of proximity effect and I wanted to see if I was correct here. Can someone confirm that I'm not off my gourd?

Essentially a general rule of thumb is the larger the diaphragm, the more pronounced proximity effect will be and the sooner it will begin to occur. Correct?

The law of inverse square would dictate that the closer the distance between mic and source, the lower the relative distance for frequency dropoff (doubling of distance = roughly 6dB in amplitude reduction).

So to get 6dB reduction in sound pressure, we go from 1cm to 2cm. Then the next 6dB reduction is 2cm to 4cm. Then 4cm to 8cm. i.e., the distance to sound reduction INCREASES for each successive 6dB reduction.

If a diaphragm is LARGER, then the sound has to travel FURTHER to reach the rear of the diaphragm as opposed to the front.

Let's use the example here: a 5cm diameter pressure-gradient diaphragm positioned 5cm away from a sound source. The sound has to travel 5cm to the front of the diaphragm, but has to travel 5cm (distance from source) + 5cm (twice the radius of the diaphragm) = 10cm to the rear of the diaphragm. Therefore, there is a DOUBLING of distance to the rear, and thus a 6dB amplitude difference across the front/rear of the diaphragm.

Second example: a 1cm diameter pressure-gradient diaphragm positioned 5cm away from a sound source. The sound has to travel 5cm to the front of the diaphragm, but has to travel 5cm (distance from source) + 1cm (twice the radius of the diaphragm) = 6cm to the rear of the diaphragm. Therefore, there is a 1.2x increase of distance to the rear, and thus a smaller amplitude difference (≈1dB?) across the front/rear of a the diaphragm.



I assume there are also other factors, like the porting slots on SDCs to make the sound travel further from front to rear, that would have a factor in proximity effect.

 

[kingkorg]

Sorry but no. By that logic you wouldn't be able to make extremely small cardioids. However there are some exceptional ones.

It is about pressure gradient, not necessarily about the distance.

You are not taking time delay network created by the backplate. The capsule hitting the rear isn't hitting the diaphragm directly, it has to go through the time delay network.

People get the impression of less proximity effect in smaller capsules usually because they have less low end, and sometimes even cut low end.

Proximity effect depends just on the pattern. However there are some very different capsules that will vary a lot in that respect.

Some mics are omni at low frequencies, cardioid above say 500hz. They have almost no proximity effect.

 

[gyraf]

Here's an article that explains pretty well why proximity effect happens as a function of the propagation difference between velocity and pressure part:

https://service.shure.com/s/article/why-does-proximity-effect-occur?language=en_US
/Jakob E.

 

[deb611]

Sorry but no. By that logic you wouldn't be able to make extremely small cardioids. However there are some exceptional ones.

It is about pressure gradient, not necessarily about the distance.

You are not taking time delay network created by the backplate. The capsule hitting the rear isn't hitting the diaphragm directly, it has to go through the time delay network.

People get the impression of less proximity effect in smaller capsules usually because they have less low end, and sometimes even cut low end.

Proximity effect depends just on the pattern. However there are some very different capsules that will vary a lot in that respect.

Some mics are omni at low frequencies, cardioid above say 500hz. They have almost no proximity effect.

On condenser capsules the time-delay of backplate, porting location on SDC mic bodies, etc. are all part of the equation surely. But what about a ribbon, which has no backplate to speak of, but rather a motor housing?

The pressure gradient between front/rear would increase based on the width of the ribbon. If you had a theoretical 5cm wide ribbon (impractical!), it would display a higher pressure gradient than a 1cm ribbon across front/rear, right?

In this case, I'm thinking more theoretically rather than practically - the diaphragm is suspended in midair with no other factors at play - and thinking about diaphragm size as the only part of the equation. The inverse square law should rule the roost here in terms of the pressure gradient at low frequencies, correct? So, as a rule in this theory - a larger diaphragm creates a longer distance for the sound to travel to hit the rear of the diaphragm - thus increasing the pressure difference between front and rear.

What am I missing here? I'm trying to connect the dots in my brain to get a better understanding of the physics, but it feels like I'm possibly missing a crucial part of the equation.

 

[kingkorg]

On condenser capsules the time-delay of backplate, porting location on SDC mic bodies, etc. are all part of the equation surely.

Well it's not just the part of the equation it is the key component, and dominant when it comes to pattern control.

50hz has the wavelength of 4 meters, 100hz 3.43 meters... what difference does it make for the low end to travel additional 5cm?

The sound is not really taking a turn and go around the diaphragm from front to back the way it's presented in most simplified diagrams.

 

[deb611]

Well it's not just the part of the equation it is the key component, and dominant when it comes to pattern control.

50hz has the wavelength of 4 meters, 100hz 3.43 meters... what difference does it make for the low end to travel additional 5cm?

The sound is not really taking a turn and go around the diaphragm from front to back.

If the mic is 5cm away from source, then inverse square law dictates that the extra 5cm would reduce the pressure by 6dB, correct? So the "what difference does an additional 5cm make" is dependent on the distance from source.

I found the graphs in gyraf's link helpful to me…I'm still not sure what I'm missing here, because by your explanation of "the sound is not really taking a turn and going around the diaphragm from front to back"…then how does a ribbon microphone function without a pressure gradient from front to back? Where's the gradient coming from, if not the distance/time travelled as the sound wave propagates across air molecules?

Once again, I feel like I'm playing connect the dots and I must be missing a dot or two…

obviously for SDCs a key to increasing the time/distance is the porting and time delay. It can be manipulated in ways other than diaphragm size…but surely the diaphragm size plays some role in it?

 

[kingkorg]

then how does a ribbon microphone function without a pressure gradient from front to back?

I think you are overcomplicating things. Of course there's pressure gradient. Pressure gradient - Pressure difference

You are standing in front of a ribbon mic, and singing into it. The pressure in front of the mic is larger than from the back.

Here's over the top example. When you say a loud "B", the sound swings the ribbon away from you. That same "B" sound is picked up by the rear of the ribbon as well, but it has way less energy so it can't fight the one coming from the front. The pressure coming from the front is larger than one coming from the back.

Now you repeat the test turning the mic by 90°. The diaphragm won't move because the pressure from the back and the front are equal.


Other extreme would be doing the similar thing with an omni mic. You say "B" in front of the mic the diaphragm goes away from you towards the backplate.

You turn the mic by 90° and the sound hits the front again from the front towards the backplate, as it cant reach the back of the diaphragm as the capsule is sealed from the back.

You turn the mic by 180°, and the sound is hiting the front yet again towards the backplate because the capsule is sealed. It is "blind" to the difference front vs back, couse it can't sense the rear pressure because it's sealed.

This is oversimplified of course because this would be example in ideal conditions. This stuff is also heavily frequency dependent. Sound is also a 3D wave going in all directions, not a straight line, simple sinusoid, or a circle.

 

[kingkorg]

Also since you mentioned the ribbon. As the ribbon is usualy about 5mm wide, it could be seen as a 5mm capsule. Dissregard the lenght of it. If what you concluded in the original post were true, the ribbon shouldn't have much of the proximity effect, yet they have tons of it.

 

[kingkorg]

One thing that you might want to dissregard is actually the sound. Or however you imagine the sound traveling through space.

The microphone doesn't have idea what a sound wave is, as far as mic is concerned there's no sound hitting it.

A microphone is nothing but a sensor, measuring pressure difference front vs back.

Imagine two isolated chambers filled with gas, with a diaphragm in between, no sound. If the pressure in the blue one is larger the diaphragm will bend towards the yellow chamber, and the other way around.

It's not the sound that moves the diaphragm, it's the pressure difference.

In ribbon mic 90° sound source situation. There is sound, it's all over the place, it can be 170db! But there is no pressure difference, so nothing happens.

 

[kingkorg]

All this said, a properly constructed directional microphone will still just measure the difference of the pressure front vs back, and this is why the size of it doesn't play a role in proximity effect.