Sounds differ in ways such as “loud/soft,” “high/low,” and “clear/muffled.” Let us express these differences using physical quantities.
Basic Knowledge
The three elements of sound:
① Loudness ← determined by amplitude (the width of vibration). Greater amplitude = louder sound.
② Pitch ← determined by frequency. Greater frequency = higher pitch.
③ Tone color ← determined by the waveform. Even at the same pitch, the waveform differs from instrument to instrument.
The unit of frequency is the hertz (Hz), which indicates how many vibrations occur in one second. The range of sounds audible to human ears is approximately 20Hz〜20000Hz(20kHz).
The wavelength λ (the length of one wave), frequency f, and speed v have the following relationship: v = fλ
Amplitude (the distance from the equilibrium position to the maximum displacement. Determines loudness)
Frequency (the number of vibrations per second. The unit is Hz )
Period T (the time required for one vibration.
T = 1/f)Wavelength λ (the length of one wave. The distance between adjacent crests)
Tone color (the quality of sound resulting from differences in waveforms. It differs among instruments)
Ultrasound・infrasound (sounds higher than 20000Hz・sounds lower than 20Hz)
Further Exploration (Background and Significance)
When observing a sound waveform with an oscilloscope, vibrations can be viewed as a graph over time. Even for the same note “A” (frequency 440Hz), the waveforms of a piano, violin, and flute differ, producing differences in tone color.
The A in the middle of a piano (A4) is 440 Hz, and the frequency doubles with each octave increase (A5=880Hz, A6=1760Hz...). This physically explains the musical phenomenon that “doubling the frequency gives the same note name.”
Ultrasound above 20000Hz is used by dolphins and bats for recognition and in echography, while infrasound below 20Hz is used in seismographs and to measure vibrations in industrial machinery.
- Three elements of sound: loudness・pitch・tone color
- Loudness ← amplitude
- Pitch ← frequency (Hz)
- Tone color ← waveform
- Human audible range: approximately 20Hz〜20kHz
- Wave equation:
v = fλ - One octave higher = twice the frequency (A4=440Hz, A5=880Hz)
Points to Note (Easily Confused)
① Loudness = amplitude, and pitch = frequency. “Loud” and “high-pitched” describe different physical quantities. ② Frequency f and period T are reciprocals: T = 1/f. ③ Even at the same pitch, different instruments have different waveforms; this produces different tone colors. ④ Ultrasound is a high sound that humans cannot hear (20kHz or higher), while infrasound is a low sound that humans cannot hear (20Hz or lower).
Practice
- State the unit of frequency.
- What determines the loudness of sound?
- For a sound with a frequency of 440Hz, state the frequency of the sound one octave higher.