The kora is a 21 string guitar-like instrument played in West Africa; it is made

Question

The kora is a 21 string guitar-like instrument played in West Africa; it is made from a half a gourd and has a long neck. The range of pitches is something like C3 (256 Hz) to C6 (2048 Hz). (a) If all the strings are diferent lengths, what is the ratio of the lengths of the longest string to the shortest string? (b) If all the strings are the same length and made of the same material, what is the ratio of the tension for the string with the highest pitch to that of the string with the lowest pitch?

Explanation / Answer

frequncy of string f = n*v/(2L)

for C3 = V/(2*L3) = 256 =====> L3 = v/(2*256)

for C6 = v/(2*L6) = 2048 =====> L6 = v/(2*2048)

L3 > L6

L3/L6 = 2048/256 = 8

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(b)

speed v = sqrt(T/u)

C3 = sqrt(T3/u)/(2L) ====> T3 = (C3*2*L)^2*u

C6 = sqrt(T6/u)/(2L)=====> T6 = (C6*2L)^2*u

T6/T3 = (C6/C3)^2*

T6/T3 = (2048/256)^2 = 64 <<<-----ANSWER

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