Acoustic Sound Treatment Foam Placement In Recording Studio. Part 2, Oblique Incidence

How should acoustic sound treatment foam be placed on the walls and ceiling of the recording studio? The choice of sound treatment foam and its placement should insure the best absorption and remove the most unwanted distortions.

Sound distortions such as standing waves, echoes, reverbs, are all a direct consequence of sound reflections from the walls. To minimize reflections, we need to maximize absorption in the sound dampening foam. We place sound foam panels on the walls anyways. So, it would be great to know what type of foam to use in different places to maximize absorption. This is the purpose of our investigation in this post.

Computer Simulations Of Different Acoustic Sound Treatment Foam Types

We have simulated oblique incidence of sound for a good number of different sound treatment foams. These are: flat sound treatment foam, narrow wedge sound treatment foam, regular wedge foam, and vertical wedge foam. Let’s look at the results.

We Discussed Normal Angle Of Incidence Before

When absorption coefficients are reported in standardized measurements, they always only include predominantly normal incidence results. We presented investigations of various types of sound treatment foams under normal incidence in a previous post. Check it out here: Soundproof Foam Panels Placement, Normal Incidence. Here we go beyond normal incidence onto sound acoustic foam. We investigate a wide range of oblique angles of incidence from 15 degrees off normal to 75 degrees off normal.

Here We Discuss Oblique Angles Of Incidence

Simulations of different angles of incidence are important because the sound from a sound source hits the walls of the recording studio at different angles. The angle depends both on the location of the foam on the wall and the location of the sound source. It makes sense that we would want to position different types of sound treatment foam at different locations to maximize absorption.

We simulate reflections, refractions, including internal reflections inside several different types of sound treatment foam at different angles of incidence.

The angles include 15 degrees, 30 degrees, 45 degrees, 60 degrees and 75 degrees off the normal. We comment on absorption and diffusion of sound. Both are important components, and both contribute to absorption and overall sound treatment.

The assumptions are as before, given here: Soundproof Foam Panels, Normal Incidence. Our simulations simulate sound with the speed of sound of 140 m/s in the foam. We assume speed of sound in air to be 330 m/s. These conditions are accurate for sound with the frequency of about 240 Hz. This is a very relevant frequency as discussed here. In acoustic sound foam, typically, the speed of sound will vary with frequency. Speed of sound will decrease with the decreasing frequency, as we explained here: Soundproof Foam Panels Placement, Normal Incidence. We expect the results at frequencies even lower than 240 Hz and speed of sound even lower than 140 m/s to possibly present additional surprises, but for now the speed of sound is fixed to 140 m/s in our simulations.

Best Sound Acoustic Foam For Incident Sound At 15 Degree Incidence

For the 15 degree sound wave incidence angle, the narrow wedge sound foam and the vertical wedge sound foam outperformed other geometries.

Narrow Wedge Sound Treatment Foam Results For 15 Degree Incidence

Figure below

 

shows a 15 degree incidence angle sound wave impinging on the right hand side of a narrow wedge sound treatment foam.

The refracted part of the ray, similar to results for normal incidence here, first internally reflects off the bottom of the foam, then internally reflects again and makes a whole up-and-down loop within the foam, then another up-and-down full loop. Effectively, the sound wave travels quite a long distance through the foam, and is therefore significantly absorbed.

The diffusion of the reflected waves from the narrow wedge sound treatment foam is excellent. There are at least 10 different directions in which the reflected wave leaves the foam and enters back into the room, as seen in our figure above.

Vertical Wedge Sound Dampening Foam Absorption And Diffusion Results For 15 Degree Incidence

Figure below

shows that a portion of the incoming wave impinging on the vertical side of the wedge refracts and travels nearly horizontally through the foam. Such long path of travel through the foam translates into higher absorption.

A part of the wave that reflects off of the vertical side of the wedge however, impinges on the inclined part of the wedge, and travels a short distance about vertically, and then exits the foam after reflecting off of the bottom. The path of the reflected part of the wave through the foam is therefore not that long.

The diffusion of the wave reflected from the vertical wedge sound dampening foam can be inferred from the above image as well. The initially refracted part of the impinging wave eventually finds its way out of the foam, but nearly straight backward. The initially reflected part of the wave is reflected back at a different angle, but that seems to be all the diffusion there is.

So at the 15 degree angle incidence, the vertical wedge sound dampening foam performs well for absorption at frequencies around 250 Hz, but not as well as the narrow wedge foam. The vertical wedge foam also exhibits lesser diffusion based on our simulations.

Best Acoustic Sound Foams For Reflection And Diffusion At 30 Degree Incidence

Vertical Wedge Acoustic Sound Foam Performance At 30 Degree Incidence

Vertical wedge acoustic sound foam performed best of all sound foam geometries in our simulations at the 30 degree incident angle. Figure below

 

shows a sound ray impinging on the vertical side of the vertical wedge sound dampening foam panel. As we can see, a good portion of the wave will refract into the foam and then internally reflect off of the right side of the wedge, then reflect off the bottom of the foam, and then hit the left side of the foam four wedges away, internally reflect back, and finally exit from the foam.

We can also see that various rays that will come out will have many different directions, as many as six or more. This indicates great diffusion of the vertical wedge acoustic sound foam panel.

Narrow Wedge Sound Treatment Foam Performance At 30 Degree Incidence

Figure below

 

shows refraction into and reflection off of the narrow wedge sound treatment foam, which performed second best of all foams simulated. We can see the path of the typical refracted wave first refract into the foam, then internally reflect off the bottom of the foam, and then exit the foam on the left in a symmetric fashion.

The initially reflected wave enters the foam through the neighboring wedge, and then internally reflects off the right wall, bottom wall, and then exits on the left at a different angle.

A significant number of reflected/refracted waves travel through the foam in various ways, even in one or more loops, and then exit at a variety of angles. We can count as many as ten different directions in which the sound waves exit the foam. However, the most prominent exit wave is the one that reflects only once off the bottom and then exits on the left. So diffusion of narrow wedge acoustic treatment foam at 30 degree incidence is significant if not perfect.

Best Sound Foam For 45 Degree Incidence

Vertical Wedge Sound Foam Shows Best Absorption And Diffusion

Figure below

 

shows why vertical wedge sound foam is the best performing foam for maximal absorption and diffusion. When the incidence is from the vertical side of the foam, the refracted wave internally reflects off of the slanted side of the wedge, then bounces off the bottom, and the internal reflection off the bottom is then reflected internally from the slanted slope to return and make one more trip down and up the foam. This significantly increases the traveling path of the wave and thus absorption.

In addition, the diffusion of the waves from the vertical foam is significant, in the figure above we can count at least six different directions in which the reflected waves are traveling back into the room.

Narrow Wedge Sound Foam Panel Is The Runner Up For 45 Degree Incidence

Figure below

 

shows why narrow wedge sound foam panel is the runner-up for the best absorption and diffusion performance among the various geometries of sound foam panels. Initially refracted wave first internally reflects off the opposite side, then internally reflects off the bottom, and finally exits the foam in a symmetric fashion. However, the initially reflected wave hits the opposite side of the wedge, refracts, and enters into the neighboring wedge at an almost normal incidence. Then, it internally reflects from the other side of the neighboring wedge, internally reflects off the bottom of the foam, and then internally reflects off of the side of a wedge, and makes another round through the foam. This causes the traveling path to be quite long and provides for high absorption.

As for the diffusion, we can count at least a dozen different directions into which reflected and refracted/reflected waves exit the foam back into the room. The narrow wedge sound foam will provide excellent sound diffusion.

Incident Angle 60 Degrees: Best Absorbing And Diffusing Sound Foam Panels

Narrow Wedge Sound Foam Panel Wins

Figure below

 

shows the 60 degree incidence of a wave onto the side of the narrow wedge sound foam. The initially refracted wave proceeds to internally reflect off of the opposite side of the wedge, then internally reflects off of the bottom of the wedge, and then makes at least one if not two or three internal loops internally reflecting/refracting through the wedges, and internally reflecting off the bottom of the sound foam panel. This provides for an extremely long path through the foam and great absorption.

Similarly, diffusion is excellent. We can count at least 14 different directions into which the reflected waves travel back into the room.

Vertical Wedge Sound Foam Panel, The Runner Up For 60 Degree Incidence

Vertical wedge sound foam panel reflections and refractions after the 60 degree incidence are shown in the figure below.

The incidence should be from the vertical side of the wedge for vertical foam panel to be effective. In the Figure we see the initially refracted wave to internally reflect off of the slanted side of the vertical wedge, then internally reflect off of the bottom of the foam, internally reflect off of the slanted side of another wedge next, internally reflects off the bottom again, and finally exits the foam. Such long path inside the sound foam panel assures good absorption.

As for diffusion, there are at least 9 different angles into which the sound reflects back in the room. That indicates solid diffusion.

Best Acoustic Sound Foams For 75 Degree Incidence

Narrow Wedge Sound Foam, Best Absorption And Diffusion At 75 Degree Incidence

Figure below

 

shows a 75 degree incidence of a sound wave onto the narrow wedge sound foam. The initially refracted wave proceeds to internally reflect off of the opposite side of the narrow wedge. It then internally reflects off the bottom of the foam. Then, that wave proceeds to internally reflect off of the wedge two removed from the original wedge. It then refracts through the wedge one removed from the original wedge. Finally, that sound wave makes one more circle through the depth of the foam. First, the wave internally reflects off of the original wedge. Then it reflects off of the bottom of the foam. Then it reflects off of the wedge one removed from original. Finally it exits the foam.

As for diffusion, we can see at least eleven directions in which the parts of the wave reflect back into the room, signifying solid sound diffusion.

Vertical Wedge Foam: Runner Up At 75 Degree Incidence Into Vertical Edge

Figure below

shows an interesting pattern of internal reflection for 75 degree incidence. This pattern occurs when the sound impinges onto the vertical edge. First, the initially refracted wave internally reflects off of the slanted side of the wedge. Then, the wave internally reflects off of the flat bottom of the foam. Then, it internally reflects off of the wedge three removed from the original wedge. Subsequently, it internally reflects off the bottom of the foam. Finally, it exits the foam. These two back-and-forth reflections cause the path of the wave to be quite long, which should assure good absorption.

In line with multiple internal reflections, the corresponding diffusion pattern shows at least 9 different directions in which the wave reflects back into the room, none of which is dominant. This warrants above average diffusion.

Conclusion: Best Acoustic Sound Foams For Different Angles Of Incidence

We simulated sound waves impinging on a variety of sound foams at different angles of incidence. Our simulations were done assuming speed of sound of 140 m/s in the foam and 330 m/s in the surrounding air. Frequencies of sound around 240 Hz propagate with such speeds in foam and air. As foams will be placed on the walls and possibly ceilings, each soundproofing foam panel will have a different angle of incidence from the sound source.

We define angle of incidence to be the angle between the incoming sound ray and the normal to the flat bottom of the acoustic sound foam.

You will have to estimate that angle of incidence of the sound. One line of the angle should go from the sound source to the point on the wall. The other line should be normal to the wall at that point. You should then pick the type of foam that absorbs and diffuses best for that angle of incidence.

We simulated here the normal incidence where angle of incidence is zero.  We also simulated oblique incidence where angle of incidence was 15, 30, 45, 60, and 75 degrees. Based on the highest absorption in the foam and best diffusion of sound reflected back, two clear winners emerge.

Vertical Wedge Sound Foam Wins At Small Angles Of Incidence

For normal incidence up to 15 degree incidence, the best performing geometry is vertical wedge acoustic foam. The vertical side must be facing toward the source of sound.

Our simulations showed that, with these geometries, the sound will make as many as two or more round trips between the shaped surface and the flat bottom of the foam. In addition, that path is not straight up and down. Instead, it involves a significant, long path, in general left-right direction parallel to the bottom of the foam. This long a path is the reason for higher absorption. See, figures above under 15 degree incidence.

Likewise, such long path in a variety of directions reflects and refracts several times, going from air to foam and back several times. Each such transmission gives rise to both reflected wave and refracted wave. This great number of reflections and refractions on multiple surfaces, in turn, contributes to high diffusion of the waves that ultimately reflect back into the room.

Narrow Wedge Sound Foam Wins For Intermediate Angles Of Incidence

Foam panel of a narrow wedge  type has a geometry with the top angle less than 60 degrees. An example of narrow wedge foam is soundproofing foam Auralex Studiofoam Wedgies.  We used the term regular wedge for foams with the top angle of 60 degrees or more.

Our simulations are based on the assumed speed of sound of 140 m/s in the foam. Speed of sound in the air is assumed to be 330 m/s. The best performing foam for the intermediate angles of incidence of 30 and 45 degrees was the narrow wedge acoustic sound foam.

For these angles of incidence, the narrow wedge foam shows the desirable effect of sound being “trapped” inside the foam. There are several back-and-forth cycles that involve several paths between the bottom of the foam and the structured part. Also, there are several trips left-and-right before the sound ray finally exits the foam and returns to the room. This should provide a long path over which the absorption of sound will be significant.

Vertical Wedge Acoustic Sound Foam Best For Large Angles Of Incidence

For angles of incidence of 60 and 75 degrees, the winner, again, is the vertical wedge acoustic soundproof foam. The foam must be facing the source of sound with the vertical side. This side allows the initial wave to predominantly enter the foam with little reflection. Then, several internal reflections later, the wave again has bounced several times from the bottom of the foam and the structured top of the foam. The wave exits after spending a significant travel path in the foam. This path is much longer than the height of the foam. This assures enhanced absorption.

Diffusion of the vertical wedge sound foam is solid as well for large angles of incidence. It is, however, not as large as under other angles of incidence. The gamut of directions in which the reflected waves ultimately reflect is surprisingly wide. It includes angles of reflection from normal to grazing, and everything in between.

We discuss best placement of acoustic sound foams further in this post: Sound Dampening Foam Panels Placement. Our findings from this post are included there.