Displacement in interfering waves¶
If two waves are traveling in the same direction and have the same amplitude, period, and wavelength (and hence the same frequency and wavenumber), but differ in the phase constant, the result is a single wave with the same period and wavelength, but its amplitude depends on the phase shift between the waves. If the shift is a multiple of \(2 \pi\), the waves are exactly in phase and their interference is fully constructive. If it is \(\pi\) plus a multiple of \(2 \pi\), they are exactly out of phase and their interference is fully destructive.
Notes:
The form of the first wave is \(u_\text{max} \sin(k x - \omega t)\) and of the second wave is \(u_\text{max} \sin(k x - \omega t + \varphi)\).
The travel of the waves in unaffected by their interference.
Conditions:
The waves are traveling in the same (or similar) directions.
They have the same amplitude, wavenumber and frequency.
Links:
- total_displacement¶
Displacement of the resulting wave.
- Symbol:
u- Latex:
\(u\)
- Dimension:
any_dimension
- amplitude¶
Amplitude of the interfering waves.
- Symbol:
u_max- Latex:
\(u_\text{max}\)
- Dimension:
any_dimension
- phase_shift¶
phase_shiftbetween the interfering waves.- Symbol:
phi- Latex:
\(\varphi\)
- Dimension:
angle
- angular_wavenumber¶
angular_wavenumberof the interfering waves.- Symbol:
k- Latex:
\(k\)
- Dimension:
angle/length
- angular_frequency¶
angular_frequencyof the interfering waves.- Symbol:
w- Latex:
\(\omega\)
- Dimension:
angle/time
- law¶
u = 2 * u_max * cos(phi / 2) * sin(k * x - w * t + phi / 2)- Latex:
- \[u = 2 u_\text{max} \cos \left( \frac{\varphi}{2} \right) \sin \left( k x - \omega t + \frac{\varphi}{2} \right)\]