Equation 1: Speed of Sound
$$c = 331.3 \sqrt{1 + \frac{T}{273.15}} + 0.6 \left(\frac{H}{100}\right) 1.2$$
Result (c):
344.0 m/s
Equation 2: Wavelength & Period
$$\lambda = \frac{c}{f} \quad \Big| \quad T_{\text{period}} = \frac{1000}{f}\text{ ms}$$
Wavelength (λ):
0.34 m
Equation 3: Transit Time
$$t = \frac{d}{c} \cdot 1000$$
Time of Flight:
29.1 ms
Equation 4: Angular Phase Difference
$$\Delta\theta = (360 \cdot f \cdot \Delta t_{\text{sec}}) \pmod{360}$$
Phase shift (Δθ):
360°
Equation 8: Vector Sum of 2 Signals
$$L_{\text{sum}} = 10 \log_{10}\left(10^{\frac{L_1}{10}} + 10^{\frac{L_2}{10}} + 2 \cdot 10^{\frac{L_1+L_2}{20}}\cos(\Delta\theta)\right)$$
Summed Level:
0.0 dB
Equation 9: Comb Filter Limits
$$\text{Peak} = 20\log_{10}(1+a) \ \Big| \ \text{Valley} = 20\log_{10}|1-a|$$
Peak / Valley:
+6.0 / -inf dB
Equation 6: Line Array Field Transition
$$d_{\text{trans}} = \frac{H^2 \cdot f}{2c}$$
Limit Distance:
5.8 m
Equation 7: Line Array Attenuation
$$Att = \begin{cases} 10\log_{10}(d) & d \le d_{\text{trans}} \\ 10\log_{10}(d_{\text{trans}}) + 20\log_{10}(d/d_{\text{trans}}) & d \gt d_{\text{trans}} \end{cases}$$
Distance Loss:
-20.0 dB
Equation 10: Sub End-Fire Alignment
$$d_{\text{ef}} = \frac{c}{4f_0} \quad \Big| \quad \tau_{\text{ef}} = \frac{d_{\text{ef}}}{c} \cdot 1000\text{ ms}$$
Rear Delay:
1.07m / 3.1ms
Equation 11: Speaker Efficiency
$$\eta = 10^{\frac{\text{Sens} - 109}{10}} \cdot 100\%$$
Efficiency (η):
3.98 %
Equation 12: Required RMS & Peak Voltage
$$V_{\text{rms}} = \sqrt{P \cdot Z} \quad \Big| \quad V_{\text{pico}} = V_{\text{rms}}\sqrt{2}$$
RMS / Peak Voltages:
44.7 / 63.2 V
Impedance / Amplifier Current
$$I_{\text{rms}} = \frac{V_{\text{rms}}}{Z}$$
Required Current:
5.59 A