In a cavity 12.5 cm by 3.9 cm, with Y being 12.5 cm and X/Z being 3.9,

[echoaa23]

In a cavity 12.5 cm by 3.9 cm, with Y being 12.5 cm and X/Z being 3.9, how would you calculate the resonance for that internal volume. The volume is filled with air and the sidewalls are not rigid. This is also assuming that one end is open.

I can, of course, give more information if it's needed...

 

[tiny-tim]

Welcome to PF!

In a cavity 12.5 cm by 3.9 cm, with Y being 12.5 cm and X/Z being 3.9, how would you calculate the resonance for that internal volume. The volume is filled with air and the sidewalls are not rigid. This is also assuming that one end is open.

I can, of course, give more information if it's needed...

Hi echoaa23! Welcome to PF!

(which end is open? )

Show us what you've tried, and where you're stuck, and then we'll know how to help you!

 

[sir-pinski]

To calculate the resonance for this internal volume, we can use the formula for the fundamental frequency of a closed-end cylindrical air column, which is f = (n/2L) * (v/λ), where n is the harmonic number, L is the length of the air column, v is the speed of sound in air, and λ is the wavelength.

In this case, n = 1 (fundamental frequency), L = 12.5 cm (length of the cavity), and v = 343 m/s (speed of sound in air at room temperature). To calculate the wavelength, we can use the formula λ = 4L/(n+1), which in this case gives us a wavelength of 50 cm.

Plugging these values into the formula, we get f = (1/2*0.125m) * (343m/s/0.5m) = 1372 Hz.

However, since the sidewalls are not rigid, the resonance frequency may be slightly different due to the flexibility of the walls. In this case, we can use the formula for the fundamental frequency of an open-end cylindrical air column, which is f = (n/2L) * (v/2L), where n is the harmonic number, L is the length of the air column, and v is the speed of sound in air.

Using the same values as before, we get f = (1/2*0.125m) * (343m/s/0.25m) = 2744 Hz.

It's important to note that these calculations are only estimates and the actual resonance frequency may vary depending on the exact dimensions and properties of the cavity. Additionally, other factors such as temperature and humidity can also affect the resonance frequency.