Standing Waves in Strings and Organ Pipes

Waves on a String

We can extend the notion of resonance to wave phenomena. Resonances during a wave medium (such as on a string or within the air, for sound) are standing waves; they’re analogous to the resonant oscillation of a mass and spring. Unlike the mass and spring that has solely one resonant frequency, a stretched string has several frequencies that are resonant. These frequencies are known as the harmonic series and are accountable for the generation of the pleasing tones from a piano, guitar, violin, or different stringed instruments. When we transfer energy to the strings of those instruments, they oscillate at the special frequencies determined by the harmonic series. When we watch the string move when it vibrates at one of the frequencies of the harmonic series, there is a standing wave pattern that is different for each frequency within the harmonic series.

Standing waves are intimately associated with the opposite wave phenomena we’ve got already mentioned. We elucidate standing waves as a superposition, or sum, of 2 traveling waves moving in completely opposite directions with the string. The traveling waves are reflected at the places wherever the string is firmly held. Since the string is held fixed at the endpoints, remember that positive wave pulses are reflected back as negative pulses.

Organ Pipe

A hollow wooden or metallic tube which is used to produce sound is called an organ pipe. It is wind instrument such as a flute, whistle, violin, clarinet, etc. their air column in it set into vibrations by blowing air into it from one end. If both ends of the pipe are open, it is called an open organ pipe: the flute is an example pipe.

Figure B

Figure A

Figure (a) is a closed organ pipe. When air is blown from the mouthpiece M, a jet of airstrikes a sharp edge L oscillating the air there and progressive sound waves travel along the pipe towards the closed end. The waves are reflected from the end and the reflected waves interfere with incident waves producing stationary waves in the pipe. Sound waves of other frequencies die out, so organ pipe can produce notes of definite frequencies depending on its length. Stationary waves are formed in an open pipe as shown in figure (b) due to reflection at the open end.

Waves in a Closed Organ Pipe

Let’s suppose there is a closed organ pipe of length L as shown in figure (a). At the open end a blast of air is blown into it and a wave, therefore, travels through the pipe and is reflected at the next end. Due to a superposition of incident and reflected waves, stationary waves are produced. In the simplest mode of vibration, there is a displacement node, N at the closed-end air is at rest there and a displacement antinode, at the open end as the air can vibrate freely.

 

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