Sound Waves: The Physics Of Sound
What is sound? Sound is a wave, a pattern—simple or complex, depending on the sound—of changing air pressure. Sound is produced by vibrations of objects. The vibrations push and pull on air molecules. The pushes cause a local compression of the air (increase in pressure), and the pulls cause a local rarefaction of the air (decrease in pressure). Since the air molecules are already in constant motion, the compressions and rarefactions starting at the original source are rapidly transmitted through the air as an expanding wave. When you throw a stone into a still pond, you see a pattern of waves rippling out in circles on the surface of the water, centered about the place where the stone went in. Sound waves travel through the air in a similar
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manner, but in all three dimensions. If you could see them, the pattern of sound waves from the stone hitting the water would resemble an expanding hemisphere. The sound waves from the stone also travel much faster than the rippling water waves from the stone (you hear the sound long before the ripples reach you). The exact speed depends on the number of air molecules and their intrinsic (existing) motion, which are reflected in the air pressure and temperature. At sea level (one atmosphere of pressure) and room temperature (20°C), the speed of sound is about 344 m/s.
Perception of a sound begins when sound pressure waves reach the tympanic membrane (eardrum), a thin, flexible membrane in the middle ear. The pressure waves cause the tympanic membrane to vibrate. The vibrations are amplified by a series of three tiny bones and transmitted to the cochlea. Curled up inside the fluid-filled, snail-shaped cochlea is the organ of Corti, where the vibrations are transduced into nerve impulses by cells called hair cells. Moving along the length of the organ of Corti, each region is sensitive to vibrations of decreasing frequency (i.e., higher pitch). The nerve impulses from the hair cells are conducted to the brain, where they are further processed, leading ultimately to the perception of sound. (Chudler, 2006; Kelly, J.P., 1991)
The wavelength is the distance (in space) between corresponding points on a single cycle of a wave (e.g., the distance from one compression maximum (crest) to the next). The wavelength (λ), frequency (f), and speed (v) of a wave are related by a simple equation: v = fλ. So if we know any two of these variables (wavelength, frequency, speed), we can calculate the third.
The mechanism that transmits the force of the pianist’s fingers on the keys to the hammers that strike the strings is called the action.
It is a complicated mechanism but, basically, here's how it works. A piano key is a long lever. Inside the piano, when you press on a key, the other end of the lever initiates two actions: 1) a damper (small felt pad that silences the string) is lifted from the string and 2) the hammer is set in motion. The hammer is not directly connected to the key, so at a certain point, it is carried forward by its own momentum, and bounces off of the string. This way, the hammer does not remain in contact with the string, which would act to dampen the vibration and silence the string. As long as you hold the key down, the damper is remains raised and the string can continue to vibrate. When you let go of the key, the damper re-contacts the string and silences it. A final detail: although the description above refers to a singular "string," only the lowest piano notes are played by single strings. In the treble range, there are three strings for each note (the hammer hits all three at once), and in the lower midrange, there are two strings for each note. The string vibrates between two fixed points: where it is stretched over the bridge and the opposite end of the string, where it is attached to the frame. The vibration results in a standing wave on the string. The fixed points of the string don't move (nodes), while other points on the string modes.
(Nave, 2006a)
The string can vibrate at several different natural modes (harmonics). Each of these vibrational modes has nodes at the fixed ends of the string. The fundamental mode has a single antinode halfway along the string. Thus, the wavelength of the fundamental vibration is twice the length (L) of the string. The second harmonic has a node halfway along the stri
manner, but in all three dimensions. If you could see them, the pattern of sound waves from the stone hitting the water would resemble an expanding hemisphere. The sound waves from the stone also travel much faster than the rippling water waves from the stone (you hear the sound long before the ripples reach you). The exact speed depends on the number of air molecules and their intrinsic (existing) motion, which are reflected in the air pressure and temperature. At sea level (one atmosphere of pressure) and room temperature (20°C), the speed of sound is about 344 m/s.
Perception of a sound begins when sound pressure waves reach the tympanic membrane (eardrum), a thin, flexible membrane in the middle ear. The pressure waves cause the tympanic membrane to vibrate. The vibrations are amplified by a series of three tiny bones and transmitted to the cochlea. Curled up inside the fluid-filled, snail-shaped cochlea is the organ of Corti, where the vibrations are transduced into nerve impulses by cells called hair cells. Moving along the length of the organ of Corti, each region is sensitive to vibrations of decreasing frequency (i.e., higher pitch). The nerve impulses from the hair cells are conducted to the brain, where they are further processed, leading ultimately to the perception of sound. (Chudler, 2006; Kelly, J.P., 1991)
The wavelength is the distance (in space) between corresponding points on a single cycle of a wave (e.g., the distance from one compression maximum (crest) to the next). The wavelength (λ), frequency (f), and speed (v) of a wave are related by a simple equation: v = fλ. So if we know any two of these variables (wavelength, frequency, speed), we can calculate the third.
The mechanism that transmits the force of the pianist’s fingers on the keys to the hammers that strike the strings is called the action.
It is a complicated mechanism but, basically, here's how it works. A piano key is a long lever. Inside the piano, when you press on a key, the other end of the lever initiates two actions: 1) a damper (small felt pad that silences the string) is lifted from the string and 2) the hammer is set in motion. The hammer is not directly connected to the key, so at a certain point, it is carried forward by its own momentum, and bounces off of the string. This way, the hammer does not remain in contact with the string, which would act to dampen the vibration and silence the string. As long as you hold the key down, the damper is remains raised and the string can continue to vibrate. When you let go of the key, the damper re-contacts the string and silences it. A final detail: although the description above refers to a singular "string," only the lowest piano notes are played by single strings. In the treble range, there are three strings for each note (the hammer hits all three at once), and in the lower midrange, there are two strings for each note. The string vibrates between two fixed points: where it is stretched over the bridge and the opposite end of the string, where it is attached to the frame. The vibration results in a standing wave on the string. The fixed points of the string don't move (nodes), while other points on the string modes.
(Nave, 2006a)
The string can vibrate at several different natural modes (harmonics). Each of these vibrational modes has nodes at the fixed ends of the string. The fundamental mode has a single antinode halfway along the string. Thus, the wavelength of the fundamental vibration is twice the length (L) of the string. The second harmonic has a node halfway along the stri