To design a vented prism speaker cabinet with the given parameters, we need to consider the volume, port dimensions, and the tuning frequency (Fs). Here's the step-by-step process:
## Cabinet Volume
Given:
- Volume = 1.54 liters = 0.0015 cubic meters
## Port Dimensions
Given:
- Port width = 38 mm = 0.038 m
To calculate the port length, we need to use the following formula:
Port Length = (Port Area × 0.0085) / (Fs × Port Width)
Where:
Assuming a square port, the Port Area = (Port Width)^2 = (0.038)^2 = 0.001444 square meters
Substituting the values in the formula:
Port Length = (0.001444 × 0.0085) / (100 × 0.038)
Port Length = 0.032 m = 32 mm
## Cabinet Dimensions
Since the cabinet is a vented prism with equilateral triangular panels, we can calculate the side length of each panel using the volume formula for a triangular prism:
Volume = (1/3) × Base Area × Height
Where:
Rearranging the formula, we get:
Height = (3 × Volume) / Base Area
Let's assume the side length of each triangular panel is 'a'.
Base Area = (√3/4) × a^2
Height = a × √(2/3)
Substituting these values in the rearranged volume formula:
a × √(2/3) = (3 × 0.0015) / ((√3/4) × a^2)
a^3 = 0.0054 / (√3/12)
a = 0.18 m = 180 mm
Therefore, the dimensions of each equilateral triangular panel are:
## Side Length: 180 mm
And the port length is:
## Port Length: 32 mm
These dimensions should provide the desired cabinet volume of 1.54 liters and a tuning frequency of 100 Hz with a port width of 38 mm.
## Cabinet Volume
Given:
- Volume = 1.54 liters = 0.0015 cubic meters
## Port Dimensions
Given:
- Port width = 38 mm = 0.038 m
To calculate the port length, we need to use the following formula:
Port Length = (Port Area × 0.0085) / (Fs × Port Width)
Where:
- Port Area is the cross-sectional area of the port (in square meters)
- Fs is the tuning frequency (in Hz)
- Port Width is the width of the port (in meters)
Assuming a square port, the Port Area = (Port Width)^2 = (0.038)^2 = 0.001444 square meters
Substituting the values in the formula:
Port Length = (0.001444 × 0.0085) / (100 × 0.038)
Port Length = 0.032 m = 32 mm
## Cabinet Dimensions
Since the cabinet is a vented prism with equilateral triangular panels, we can calculate the side length of each panel using the volume formula for a triangular prism:
Volume = (1/3) × Base Area × Height
Where:
- Base Area is the area of the triangular base
- Height is the height of the prism (perpendicular distance between the bases)
Rearranging the formula, we get:
Height = (3 × Volume) / Base Area
Let's assume the side length of each triangular panel is 'a'.
Base Area = (√3/4) × a^2
Height = a × √(2/3)
Substituting these values in the rearranged volume formula:
a × √(2/3) = (3 × 0.0015) / ((√3/4) × a^2)
a^3 = 0.0054 / (√3/12)
a = 0.18 m = 180 mm
Therefore, the dimensions of each equilateral triangular panel are:
## Side Length: 180 mm
And the port length is:
## Port Length: 32 mm
These dimensions should provide the desired cabinet volume of 1.54 liters and a tuning frequency of 100 Hz with a port width of 38 mm.