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6 Oct 2020
The low E string and the high E string on a guitar are tuned to have fundamental frequencies of 82.4 Hz and 329.6 Hz, respectively. The difference in the fundamental frequency is primarily due to the different thickness, and therefore different mass per unit length, of the two strings. We could, however, try to design a guitar using the same type of strings for both notes by varying either the length of the string or its tension.
a. If the mass per unit length and the length were kept the same for both strings, what would be the ratio of the tension in the high E string to the tension in the low E string?
b. If the mass per unit length and the tension were kept the same for both strings and we found a way to alter the length of the strings, what would be the ratio of the length of the high E string to the length of the low E string?
The low E string and the high E string on a guitar are tuned to have fundamental frequencies of 82.4 Hz and 329.6 Hz, respectively. The difference in the fundamental frequency is primarily due to the different thickness, and therefore different mass per unit length, of the two strings. We could, however, try to design a guitar using the same type of strings for both notes by varying either the length of the string or its tension.
a. If the mass per unit length and the length were kept the same for both strings, what would be the ratio of the tension in the high E string to the tension in the low E string?
b. If the mass per unit length and the tension were kept the same for both strings and we found a way to alter the length of the strings, what would be the ratio of the length of the high E string to the length of the low E string?
VikasLv10
6 Nov 2020
