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Stringed instruments are stimulated near one end to enhance the production of harmonics.

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## Stringed instruments are stimulated near one end to enhance the production of harmonics.

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**A taut wire or string that vibrates as a single unit**produces its lowest frequency, called its fundamental.**A louder sound is produced if the vibrations are transferred**to a larger surface (an impedance transformer).**Sonometer - a device for studying the properties of**vibrating strings and the sounds they produce.**The frequency of the vibrating air molecules is the same as**the frequency of the vibrating string.**The fundamental and the vibrational modes having frequencies**that are whole number multiples of the fundamental are called harmonics.**The fundamental is the first harmonic. A vibration having a**frequency twice that is the second harmonic. Three times that is the third harmonic.**Quality, or timbre makes sounds produced by different**instruments sound different even when they are producing the same tone with equal intensity.**The quality of a sound depends on the number of harmonics**produced and their relative intensities.**Stringed instruments are stimulated near one end to enhance**the production of harmonics.**The frequency of a vibrating string is determined by its**length, diameter, tension, and density.**1. Law of lengths - the frequency of a string is inversely**proportional to its length if all other factors are constant. f / f’ = l’ / l**2. Law of diameters the frequency of a string is inversely**proportional to its diameter if all other factors are constant. f / f’ = d’/ d**3. Law of tensions -the frequency of a string is directly**proportional to the square root of the tension on the string if all other factors are constant. f / f’ = √ F / √ F’**4. Law of densities - the frequency of a string is inversely**proportional to the square root of its density if all other factors are constant. f / f’ = √ D’ / √ D**A violin string is 0.035 m long and is stretched with a**tension of 27 N, so that it vibrates with a frequency of 256 Hz. What is the frequency when the length is 0.030 m and the tension is 32 N?**Resonance can be produced between a tuning fork and a column**of air.**The length of a closed tube is approximately 1/4 the**wavelength of its fundamental resonant frequency. λ ~ 4lλ = 4(l + 0.4d)λ is the wavelength of the fundamental resonant frequency,l is the length of the closed tube, and d is its diameter**A closed tube is resonant at odd quarter-wavelength**intervals. The resonant frequencies of a closed tube are harmonics, but only odd harmonics of the fundamental.**Normal oscillations of air columns are characterized by:1. a**displacement node at a closed end, and2. a displacement loop at an open end.**The length of an open tube is approximately 1/2 the**wavelength of its fundamental frequency.λ ~ 2l λ = 2(l + 0.8d)λ is the wavelength of the fundamental resonant frequency,l is the length of the closed tube, and d is its diameter**The resonant frequencies of an open tube are harmonics, and**all harmonics of the fundamental mode are present.**The quality of sounds from open tubes and closed tubes is**not the same.**Two wave trains traveling in the same direction will cause a**superposition at a given point whose amplitude varies with time.**The number of beats per second equals the difference between**the frequencies of the component waves.**The average frequency is 1/2 the sum of the two frequencies.**