Q4 points Previous Answers Tipie-6 16.P058. The G string on an instrument is 37

Question

Q4 points Previous Answers Tipie-6 16.P058. The G string on an instrument is 37 cm long, when played without fingering, it vibrates at a frequency of 1g6 Hz. Te next higher notes on the C-major scale are A ?220 ?), 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? A-32.9 My Notes Ask Your Teacher XC- ??. Determine the relationship between the fundamental frequency and the length of the string. Taking a ratio of the frequencies should yield a ratio of string lengths eBook Submit Answar Save Prograss Practice Arathar Vorsion

Explanation / Answer

fundamental frequency fo = V/2L

so V = 2L f

V = 2 * 196 * 0.37

V = 145.04 m/s

so

when f = 220 Hz

f = V/2Xa = 200 Hz

xa = V/2f

Xa = 145.04/(2 * 220)

xa = 33 cm

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for f = 247 Hz

xb = 145.04/(2 * 247)

xb 29.3 cm

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for f = 262 Hz

xc = 145.04/(2 * 262)

xc = 27.67 cm

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for f = 294 Hz

xd = 145.04/(2 * 294)

xd = 24.66 cm

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