Speed of sound is constant in surrounding environment. It surely does not change with frequency. Speed of sound in NTP is 343 m/s. On the other hand length of a sound wave varies with frequency, for example length 100Hz wave is 3,43m and 25Hz wave corresponds 13,72m. And one side of loudspeaker radiates to the narrow end called horn throat while opposite side radiates near mouth in a tapped horn. You could have checked these well known facts ie. From wikipedia if you’d like to educate people.
Education brings great responsibility. The speed of sound is related to the density of the medium through which it travels. At sea level the speed of sound is greater ( faster ) than at the top of Mount Everest. We go higher and the air becomes more rare ( less dense ) and the speed of sound gets slower. In the throat and initial expansion region of a Bass Horn we create physical boundaries.
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These boundary walls would appear to contain a fixed volume of gas. However: one of these ‘walls’ ( AKA the speaker cone ) is ‘moveable’.
When the cone moves towards or into the throat it reduces the volume of the constraining boundaries in this region. We would consider that we have increased the pressure in this ‘vessel’. We have also increased the density of the gas in this vessel. Therefore: we should be mindful that the speed of sound will also increase. When the cone moves away from the throat.the volume in the ‘region’ increases, density drops below atmospheric and speed of sound decreases.
So: speed of sound is essentially constant at Sea Level, under ‘normal conditions’. However, if we build a micro climate where we use boundaries to deliberately change the density of gas, there will be a different outcome. Hey Todd, So the geometry of the horn itself is absolutely critical to its functioning, the volume, length, and taper of the horn are all carefully tuned to the frequencies and drivers you are after. There is a little open sourced tool called that lets you model a horn and adjust the design for the results you are after. There is a learning curve, and frankly, some artistry to getting your own fold right, but you could certainly custom design around, say, a six inch driver and a narrow enclosure.
There are a few designs out there like that though. Check out the I know a guy who built a pair of those and laid them down flat on the floor under the couch so they made a little theater style riser for the couch.
Don’t hesitate to ask questions on AVS Forum too, there are a lot of amazing guys on there who know a lot more than I do. I have paypal’d beer money to a few of them for their time!