Sound Waves Between Two Walls

Version: 1.03 (2019-08-12)
Software platform: Microsoft Excel

As the title says, this software calculates the sound field of a point source placed between two parallel walls.

Software features:

Frequency response graph with adjustable time-window and octave smoothing.
Cumulative spectral decay plot (waterfall plot).
Impulse response graph.

The simulation is based on the image source model (ISM). Only the first eight reflections are computed (per wall).

simple acoustic simulator: reflections, interference patterns, standing waves between two walls, waterfall plot

This software is suitable for studying the following cases:

Steady state and transient analysis of standing waves between two parallel walls.
The effect of speaker and microphone placement (listening position) on the first reflections (To see this, select 'Time-window' on the frequency response graph and increase time-window gradually from one millisecond).
The effect of speaker and microphone placement (listening position) on the late reflections (standing wave patterns, decay of resonances in the cumulative spectral decay graph).
The effect of the wall's absorption coefficient on the late and early reflections. Late reflections are more sensitive to the value of the absorption coefficient, because the sound wave strikes the wall more times.
Not only the decay spectrum of a system can be analyzed, but the opposite: how the frequency response is taking shape as the reflections arrive at the microphone. To see this, select 'Time-window' on the frequency response graph and increase time-window gradually from one millisecond.
A real-life example: floor-ceiling reflections (or other 'two-wall' speaker-boundary interference).

Version: 1.03.
Format: xls (Microsoft Excel 2003 Workbook)
Required software: Microsoft Excel 2003 or newer
License: freeware
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Examples, case studies

(Modal analysis, room modes)

Wall distance is 3 meters, sound source x coordinate and y coordinate are zero (source is on the left wall), microphone y coordinate is zero. Reflection coefficient is one.

A simple formula for calculating the frequency of the first mode (F₀):

F₀ = 343 / 2L

L is the distance between opposite walls in meters, F₀ is the frequency of the first mode in Hz. In our case the first mode is at 57 Hz.

We will see that the excitation of room modes depends on the location of the source and microphone.

1. Microphone is on the right wall. All modes are at full amplitude:

2. Microphone is located in the middle between two walls. Only even order modes:

3. Microphone is 3 meters from the left wall, but the reflection coefficient has been changed to 0.71 (equivalent to an absorption coefficient of 0.5). Reducing the reflection coefficient has a huge effect on the level and decay of room modes. Decay increases from 22 dB / 50 ms to 40 dB / 50 ms.

4. Vertical room modes. For this, we have to rotate the side view of the room by 90 degrees: the left wall will be the floor, the right wall will be the ceiling. Since the typical ear height while sitting is approx. 1.2 meters, it's worth setting the distance of the microphone from the left wall to this value. The vertical offset is the distance from the speaker. We change the distance of the source from the left wall from 0 meter to 1.2 meter.

The decay spectrum is the best, when the speaker distance from the floor is 60 cm.
The frequency response is the smoothest, when the speaker distance from the floor is 1.2 meter. Decay spectrum contains some even order modes.