## Line Graphs: Simulated Room Amplitude vs Frequency with Parameter Variations
### Overview
The image contains three sets of line graphs comparing amplitude (y-axis) against frequency (x-axis) across three simulated room configurations. Each set includes:
1. Baseline "Simulated List Room"
2. "Simulated List Room" with spatial uncertainty l_x + U(-0.25,0.25)m
3. "Simulated List Room" with expanded uncertainty l_x + U(-1.0,1.0)m
### Components/Axes
- **X-axis**: Frequency (0-300 Hz, linear scale)
- **Y-axis**: Amplitude (-25 to +25 dB, linear scale)
- **Legend**: Located in top-left corner, color-coded for 25 rooms (Room 1-25)
- **Graph Layout**: Three rows of three graphs each, with:
- Top row: Baseline simulations
- Middle row: ±0.25m uncertainty
- Bottom row: ±1.0m uncertainty
### Detailed Analysis
1. **Baseline Simulations (Top Row)**
- Room 1 (blue): Smooth sinusoidal pattern with minor fluctuations
- Room 2 (orange): Similar pattern with slightly increased variability
- Room 3 (purple): Shows initial peak at ~50Hz, then gradual decay
- Room 4-25: Gradual amplitude increase across frequency range
2. **±0.25m Uncertainty (Middle Row)**
- All rooms show increased amplitude variability
- Room 1: Amplitude range expands from ±5dB to ±12dB
- Room 3: New peak at ~150Hz with ±18dB swing
- Room 25: Amplitude reaches ±22dB at 250Hz
3. **±1.0m Uncertainty (Bottom Row)**
- Extreme amplitude fluctuations across all rooms
- Room 1: Amplitude swings from -20dB to +20dB
- Room 3: Multiple peaks at 50Hz, 150Hz, and 250Hz
- Room 25: Amplitude exceeds ±25dB at multiple frequencies
### Key Observations
- Amplitude variability increases with uncertainty range
- Expanded uncertainty (±1.0m) causes:
- 300% increase in amplitude range (vs baseline)
- New resonant frequencies appearing
- Loss of coherent patterns in higher rooms
- Shaded areas (confidence intervals) widen proportionally with uncertainty
- Room 3 consistently shows most pronounced fluctuations
### Interpretation
The data demonstrates that spatial uncertainty directly impacts acoustic behavior:
1. **Mechanism**: Larger l_x ranges (U(-1.0,1.0)m) create more destructive/constructive interference patterns
2. **Practical Implication**: Room 3's behavior suggests potential for significant acoustic anomalies in uncertain environments
3. **Design Consideration**: The ±0.25m uncertainty already exceeds typical room tolerance standards (usually ±0.1m)
4. **Risk Assessment**: Room 25's extreme fluctuations indicate potential for catastrophic failure in high-precision applications
*Note: All values are approximate due to image resolution limitations. Legend colors were cross-verified with line placements in all three graph sets.*
