Question

The G string on a violin is 30 cm long. when played without fingering, it vibrates at frequency 196 Hz. The next higher notes on the scale are A(220 Hz), B(247 Hz), C(262 Hz), and D(294 Hz). How far from the end of the string must a finger be placed to play these notes?

Answer 1

Here,

for the frequency without fingering

v/(2L) = 196

where L = 30 cm

hence, v = 196 * 0.60 m/s

v = 117.6 m/s
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Now, for 220 Hz, let the finger is placed at x distance

v/(2(L - x)) = 220

117.6/(2(0.30 - x)) = 220

solving for x

x = 0.033 m = 3.3 cm

the finger shall be placed 3.3 cm away
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Now, for 247 Hz, let the finger is placed at x distance

v/(2(L - x)) = 247

117.6/(2(0.30 - x)) = 247

solving for x

x = 0.062 m = 6.2 cm

the finger shall be placed 6.2 cm away

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Now, for 262 Hz, let the finger is placed at x distance

v/(2(L - x)) = 262

117.6/(2(0.30 - x)) = 262

solving for x

x = 0.076 m = 7.6 cm

the finger shall be placed 7.6 cm away

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Now, for 294 Hz, let the finger is placed at x distance

v/(2(L - x)) = 294

117.6/(2(0.30 - x)) = 294

solving for x

x = 0.1 m = 10 cm

the finger shall be placed 10 cm away