Question

what is the sum of room modes if the room 15 meters length 7 meters width and 4 meters hight?

Answer 1

Answer on Question#40649 - Math - Geometry

what is the sum of room modes if the room 15 meters length 7 meters width and 4 meters hight?

Solution:

Room modes are caused by reflections between room surfaces. There are three types of modes in a rectangular room: axial (sound waves reflecting between two parallel surfaces), tangential (sound waves reflecting between four surfaces), and oblique (sound waves reflecting between all six surfaces). Axial modes have the most influence on the acoustical characteristics of the room. Oblique modes have less effect than the other two.

Axial

Tangential

Oblique

To calculate the frequencies of the axial, oblique und tangential modes, use the following equation:

$$f = \frac {c}{2} \sqrt {\left(\frac {n _ {x}}{L}\right) ^ {2} + \left(\frac {n _ {y}}{B}\right) ^ {2} + \left(\frac {n _ {z}}{H}\right) ^ {2}}$$

$f =$ Frequency of the mode in Hz

$c =$ Speed of sound $343\mathrm{m / s}$ at $20^{\circ}\mathrm{C}$ $(68^{\circ}\mathrm{F})$

$n_x =$ Order of the mode of the room length

$n_y =$ Order of the mode of the room width

$n_z =$ Order of the mode of the room height

L, B, H = Length, width, and height of the room in meters

$$\mathrm {L} = 1 5 \mathrm {m}, \mathrm {B} = 7 \mathrm {m}, \mathrm {H} = 4 \mathrm {m}$$

Axial room modes

Tangential room modes

Oblique room modes