17.13
Batidas
O estudo da música fornece muitos exemplos da sobreposição de ondas e da interferência construtiva e destrutiva. Pouquíssimos exemplos de música sendo…
Quando duas ondas sonoras de igual amplitude e frequências ligeiramente diferentes interferem uma na outra, a equação de deslocamento para a onda resultante em uma determinada posição pode ser determinada. Sua intensidade aumenta e diminui alternadamente com o tempo.
O comprimento total do eixo do tempo representa um segundo. Quando as duas ondas estão em fase, suas amplitudes aumentam.
E, quando as duas ondas estão exatamente fora de fase, a amplitude total é zero.
Essa variação periódica na intensidade do som com o tempo forma batidas.
A onda resultante se parece com uma única onda senoidal com amplitude variável, que passa por dois máximos e dois mínimos em um segundo. A frequência dessa variação de amplitude é de dois hertz.
O número de batimentos ouvidos por segundo é chamado de frequência de batimento e é igual à diferença de frequência das ondas sonoras.
O intervalo de tempo entre duas batidas sucessivas é definido como o período de batida, que é o inverso da frequência de batimento.
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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.