This assignment, you submit answers by question parts The number of submissions

Question

This assignment, you submit answers by question parts The number of submissions remaining for each question part only changes if you submit or the best submission for each question part is used for your score The G string on an instrument Is 50 cm long. When played without fingering, It vibrates at a frequency of 196 Hz. The next higher notes on the C-major scale are A (220 Hz). B (247 Hz), C (262 Hz), and D (294 Hz). What distance x from the end of the string must a finger be placed to play each of these notes? x_A = 26.73 cm x_B = cm x_c = cm x_D = cm Determine the relationship between the fundamentals frequency and the length of the string. Taking a ratio of the frequencies should yield a ratio of string lengths.

Explanation / Answer

The frequency of the stretched string is given by

f = 1/2L * sqrt(T/mu)

mu = mass per unit length

T = tenstion

for whole length

196 = (1/2*0.5m )*sqrt(T/mu)

sqrt(T/mu) = 196 m/s

for A point

220 = 1/2*xa * 196

xa = 196/2*220

xa = 44.5 cm

for poitn B

f = (1/2*xb)*sqrt(T/mu)

247 = (1/2*xb)*196

xb = 39.68 cm

for point C

262 = (1/2*xc)* 196

xc = 37.4 cm

for point D

294 = (1/2*xd)*196

xd = 33.3 cm

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