17.13
Les battements
L'étude de la musique offre de nombreux exemples de la superposition d'ondes et de l'interférence constructive et destructive qui en résulte. Très peu…
Lorsque deux ondes sonores d’amplitude égale et de fréquences légèrement différentes interfèrent l’une avec l’autre, l’équation de déplacement de l’onde résultante à une position particulière peut être déterminée. Son intensité augmente et diminue alternativement avec le temps.
La durée totale de l’axe temporel représente une seconde. Lorsque les deux ondes sont en phase, leurs amplitudes s’additionnent.
Et, lorsque les deux ondes sont exactement déphasées, l’amplitude totale est nulle.
Cette variation périodique de l’intensité sonore avec le temps forme des battements.
L’onde résultante ressemble à une onde sinusoïdale unique d’amplitude variable, qui passe par deux maxima et deux minima en une seconde. La fréquence de cette variation d’amplitude est de deux hertz.
Le nombre de battements entendus par seconde est appelé fréquence de battement et est égal à la différence de fréquence des ondes sonores.
L’intervalle de temps entre deux battements successifs est défini comme la période de battement, qui est l’inverse de la fréquence du battement.
View the full transcript and gain access to JoVE Core videos
Q1: What happens when two sound waves of slightly different frequencies interfere with each other?
When two sound waves of equal amplitude and slightly different frequencies interfere, their displacement creates a resultant wave with varying amplitude. The intensity rises and falls alternately as the waves move in and out of phase. This periodic variation in sound intensity with time forms beats, producing a single sinusoidal wave that appears to pulse in loudness.
Q2: How is beat frequency defined and calculated?
Beat frequency is the number of beats heard per second and equals the difference between the frequencies of the two interfering sound waves. For example, if one wave has a frequency of 440 Hz and another has 442 Hz, the beat frequency is 2 Hz. The beat period, which is the time interval between successive beats, is the inverse of the beat frequency.
Q3: Why do beats occur when sound waves are in and out of phase?
Beats result from constructive and destructive interference between waves. When the two waves are in phase, their amplitudes add together, creating maximum intensity. When exactly out of phase, the total amplitude becomes zero. This alternating pattern of constructive and destructive interference produces the characteristic amplitude variation that creates the beating sound effect.
Q4: What does the resultant wave look like when beats are formed?
The resultant wave appears as a single sinusoidal wave with varying amplitude that goes through two maxima and two minima in one second when the beat frequency is 2 Hz. The wave oscillates between loud and quiet, with the amplitude envelope rising and falling periodically. This creates the characteristic pulsing or throbbing sound that listeners perceive as beats.
Q5: How do piano tuners use beats to tune instruments?
Piano tuners strike a tuning fork and play a note on the piano simultaneously. As they adjust the piano string, the beat frequency decreases as the note's frequency approaches the tuning fork's frequency. When the frequencies match, the beats disappear entirely. This method works because beats between two tones can be heard up to approximately 6 or 7 Hz, making small frequency differences audible.
Q6: Why must multi-engine aircraft propellers be synchronized?
If propeller frequencies are not synchronized, the sound waves from different engines interfere and create annoying beats heard as loud throbbing sounds. Synchronization prevents this unwanted beat phenomenon. Some aircraft use electronic systems for synchronization, while others rely on pilots adjusting engine speeds by ear, similar to the piano tuning process.
Q7: What role does constructive and destructive interference play in creating beats?
Beats are a direct result of constructive and destructive interference between two slightly different frequencies. Constructive interference occurs when waves align, amplifying the sound, while destructive interference occurs when they oppose each other, reducing the sound. The periodic cycling between these two interference states creates the amplitude modulation characteristic of beats.