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Ratio, Proportion, and Variation

Identify variations from word problems

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Credit: Steve Snodgrass
Source: http://www.flickr.com/photos/stevensnodgrass/3874128759/
License: CC BY-NC 3.0

Violins and cellos are both string instruments, which means that they both produce sound due to vibrating strings. So how do they still produce such different sounds?

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A string vibrating at a low frequency will produce a lower pitch than a string vibrating at a high frequency. The tension, length, and thickness of a vibrating string all influence the frequency of that particular string. The length of the string and the thickness of the string are both inversely related to the vibrating frequency. As the length or thickness of the string increases, the frequency of vibration decreases, resulting in a lower pitch.

Credit: Laura Guerin
Source: CK-12 Foundation
License: CC BY-NC 3.0

How are these inverse relationships used in producing music? If you examine the difference between a violin and a cello, you will see that the strings on the cello are both longer and thicker than those on the violin. Thus, the cello has a lower pitch than the violin. With any given string instrument, a musician can also apply this knowledge of the inverse variation between a string’s length and its vibrating frequency (and thus pitch) as he or she fingers the strings. When different lengths of a certain string are allowed to vibrate, different pitches will be heard.

See for yourself: https://www.youtube.com/watch?v=RxFNHeXKmrY

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Learn more about frequency and pitch at the link below.


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  1. [1]^ Credit: Steve Snodgrass; Source: http://www.flickr.com/photos/stevensnodgrass/3874128759/; License: CC BY-NC 3.0
  2. [2]^ Credit: Laura Guerin; Source: CK-12 Foundation; License: CC BY-NC 3.0

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