17.13
ビート
音楽の研究では、波の重ね合わせや、それによって生じる建設的および破壊的な干渉の例が数多く提供されています。 単一のソースが単一の周波数を長時間再生することで演奏される音楽の例はほとんどありません。 単一周波数の音を長時間続けると、航空機のエンジンや大音量のファンの不要な騒音と同様に、イライラするほど…
振幅が等しく、周波数がわずかに異なる2つの音波が互いに干渉する場合、特定の位置で生じる波の変位方程式を決定できます。その強度は時間とともに交互に増減します。
時間軸の全長は 1 秒を表します。2つの波が同相の場合、振幅は加算されます。
また、2つの波が正確に位相がずれている場合、合計振幅はゼロになります。
この時間による音の強度の周期的な変化がビートを形成します。
結果として生じる波は、振幅が変化する単一の正弦波のように見え、1秒間に2つの最大値と2つの最小値を通過します。この振幅変動の周波数は2ヘルツです。
1秒間に聞こえるビート数はビート周波数と呼ばれ、音波の周波数の差に等しくなります。
2 つの連続するビート間の時間間隔は、ビート周波数の逆数であるビート周期として定義されます。
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.