Parameters
Presets
Wave 1 (Cyan)
Amplitude A₁
1.00
Frequency f₁
5.0 Hz
Phase φ₁
0°
Wave 2 (Orange)
Amplitude A₂
1.00
Frequency f₂
6.0 Hz
Phase φ₂
0°
Wave Speed v
5.0 m/s
—
Beat Frequency [Hz]
—
Max Combined Amplitude
—
Wavelength λ₁ [m]
—
Wavelength λ₂ [m]
Wave 1 — y₁ = A₁ sin(k₁x − ω₁t + φ₁)
Wave 2 — y₂ = A₂ sin(k₂x − ω₂t + φ₂)
Superposed Wave — y = y₁ + y₂
Theory
$$y_1 = A_1\sin(k_1 x - \omega_1 t + \phi_1), \quad k_i = \frac{2\pi f_i}{v}$$ $$y_2 = A_2\sin(k_2 x - \omega_2 t + \phi_2)$$ $$y = y_1 + y_2 \quad \text{(Principle of Superposition)}$$Beat frequency: $f_{beat} = |f_1 - f_2|$
Standing wave: Counter-propagating waves of equal frequency → $y = 2A\cos(kx)\sin(\omega t)$
CAE Applications: Interference pattern computation in acoustic FEM / Active Noise Cancellation (ANC) design / Phased array techniques in ultrasonic testing / Resonance avoidance in structural vibration design.