17.13
비트
음악 연구는 파동의 중첩과 발생하는 건설적 및 파괴적 간섭에 대한 많은 예를 제공합니다. 연주되는 음악의 예는 오랜 시간 동안 단일 주파수를 재생하는 단일 소스로 구성됩니다. 장기간 동안 단일 주파수의 소리는 항공기 엔진의 원치 않는 소음이나 시끄러운 팬과 유사하게 짜…
동일한 진폭과 약간 다른 주파수의 두 음파가 서로 간섭할 때, 특정 위치에서 결과 파동에 대한 변위 방정식을 결정할 수 있습니다. 그 강도는 시간에 따라 번갈아 상승하고 감소합니다.
시간 축의 총 길이는 1초를 나타냅니다. 두 파동이 위상이 같으면 진폭이 추가됩니다.
그리고 두 파동이 정확히 위상을 벗어났을 때 총 진폭은 0입니다.
시간에 따른 소리 강도의 주기적인 변화는 비트를 형성합니다.
결과 파동은 다양한 진폭을 가진 단일 정현파처럼 보이며 1초에 2개의 최대값과 2개의 최소값을 통과합니다. 이 진폭 변화의 주파수는 2헤르츠입니다.
초당 들리는 비트의 수를 비트 주파수라고 하며 음파의 주파수 차이와 같습니다.
두 개의 연속적인 비트 사이의 시간 간격은 비트 주기로 정의되며, 이는 비트 주파수의 역입니다.
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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.