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प्रश्न
Answer in brief:
What are harmonics and overtones?
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उत्तर
A stationary wave is formed in a bounded condition, with the boundary being either rigid support or a free end. The boundary conditions restrict the possible stationary waves and allow only a discrete set of frequencies.
The fundamental frequency of vibration is the lowest allowed frequency, n1. Harmonics are integral multiples of the fundamental frequency. The harmonics may or may not be present in the sound so produced. The first harmonic is defined as the fundamental frequency. The second harmonic is 2n1, which is twice the fundamental, and the third harmonic is 3n1, and so on.
Consider a vibrating string. The modes of vibration are all multiples of the fundamental and are related to the string length and wave velocity. Higher frequencies are found via the relationship fn= nf1, wavelength = `2"L"/"n"` where L is the string length.
An overtone is a name given to any resonant frequency above the fundamental frequency or fundamental tone. The first permitted frequency over the fundamental is termed the first overtone, the next higher frequency is called the second overtone, and so on. The list of successive overtones for an object is called the overtone series. The first overtone as well as all subsequent overtones in the series may or may not be an integer multiple of the fundamental. Sometimes the relationship is that simple, and other times it is more complex, depending on the properties and geometry of the vibrating object.
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संबंधित प्रश्न
A sound wave in a certain fluid medium is reflected at an obstacle to form a standing wave. The distance between two successive nodes is 3.75 cm. If the velocity of sound is 1500 m/s, find the frequency.
A pipe closed at one end can produce overtones at frequencies 640 Hz, 896 Hz, and 1152 Hz. Calculate the fundamental frequency.
Find the fundamental, first overtone, and second overtone frequencies of a pipe, open at both the ends, of length 25 cm if the speed of sound in air is 330 m/s.
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[Hint: Remember that the moving end is an antinode.]
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Distinguish between an overtone and harmonic.
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