Sound is a longitudinal wave (compressional wave) that uses air as its medium. Let us understand the physical meanings of the pitch, loudness, and timbre of sound.
Basic Knowledge
Correspondence between the three elements of sound and physical quantities:
・Pitch ← frequency (Hz): The greater the frequency, the higher the pitch
・Loudness ← amplitude: The greater the amplitude, the louder the sound
・Timbre (timbre) ← waveform (composition of overtones): Even at the same pitch, instruments have different overtones
Frequency range audible to humans (audible range): about 20 Hz ～ 20000 Hz
・Below 20 Hz: low-frequency sound; above 20000 Hz: ultrasound
Speed of sound:
・In air (15°C): about 340 m/s
・The higher the temperature, the faster it travels: v ≒ 331 + 0.6t [m/s] (t: temperature ℃)
・It travels faster in solids > liquids > gases (the more rigid the medium, the faster it travels)
Beats (beat): When two sounds with slightly different frequencies are produced simultaneously, the sound periodically becomes louder and softer. Number of beats per second = |f₁ − f₂|
Audible range（The frequency range humans can hear: 20 Hz ～ 20000 Hz）
Ultrasound（20000 Hz or higher. Used for medical diagnosis, fish finders, and so on）
Three elements of sound（Pitch, loudness, and timbre）
Beats (beat)（Interference between two sounds with slightly different frequencies. Number of beats per second = |f₁ − f₂|）
Resonance (resonance)（A phenomenon in which vibration becomes large when sound has the same frequency as the natural frequency）
Resonance of an air column（Resonance occurs when the length of a tube matches the wavelength）
Further Study (Background and Significance)
Resonance conditions for an air column:
・Open pipe (open at both ends): Antinodes at both ends. Resonance condition L = nλ/2 (n = 1, 2, 3…)
・Closed pipe (closed at one end): A node at the closed end and an antinode at the open end. Resonance condition L = (2n−1)λ/4 (n = 1, 2, 3…)
Only odd-numbered overtones are produced in a closed pipe.
Assuming a sound speed of c = 340 m/s, the wavelength of a 440 Hz sound (the note A) is λ = 340/440 ≒ 0.77 m. For this sound to vibrate in its fundamental mode in a closed pipe, L = λ/4 ≒ 0.19 m is required. The lengths of wind instruments are determined by this principle.
Beats are used to tune musical instruments. When a reference tone of 440 Hz and a slightly different tone sound together, beats are heard, and the instrument is adjusted until the number of beats becomes 0.
In medical applications of ultrasound (echo examinations), ultrasound is sent into the body and reflected waves are analyzed to create images of a fetus and the condition of organs.
- Pitch ← frequency
- Loudness ← amplitude
- Timbre ← waveform (composition of overtones)
- Speed of sound: about 340 m/s in air; depends on temperature
- Sound travels faster in solids > liquids > gases
- Number of beats = |f₁ − f₂| [times/s]
- Open pipe: L = nλ/2; closed pipe: L = (2n−1)λ/4
Important Notes (Common Confusions)
① “High sound” means high frequency (unrelated to amplitude), while “loud sound” means large amplitude (unrelated to frequency). ② Sound travels faster at higher temperatures. Its speed changes according to the type and condition of the medium. ③ Do not confuse the resonance conditions of open and closed pipes. A closed pipe produces only odd-numbered overtones. ④ Beats are determined by the absolute value of the difference; it does not matter which frequency is higher.
Practice
- Sounds with frequencies of 442 Hz and 438 Hz are produced simultaneously. Find the number of beats per second.
- Approximately how many m/s is the speed of sound in air?
- Which element of a wave determines the loudness of sound?