Answer to Question #168193 in Physics for Shem

Question

In this activity, we are to look at the strings of an acoustic guitar. The strings are

normally stretched to a length of 62.1 cm. In the standard tuning, the open note strings

are adjusted to have the following pitches:

1st string – E4 (330 Hz)

2nd string – B3 (247 Hz)

3rd string – G3 (196 Hz)

4th string – D3 (147 Hz)

5th string – A2 (110 Hz)

6th string – E2 (82.4 Hz)

1. Calculate the wave velocity (in cm/s) of each string in the standard tuning. (18

pts)

2. Notes other than the open string notes shown above are played by pressing the

string on the fretboard, which effectively reduces the length of the string while

keeping the wave velocity unchanged.

a. Find the length of the specified string needed to play the following notes.

(18 pts)

i. 1st string – A4 (440 Hz)

ii. 2nd string – A4 (440 Hz)

iii. 3rd string – A4 (440 Hz)

iv. 4th string – A3 (220 Hz)

v. 5th string – A3 (220 Hz)

vi. 6th string – A3 (220 Hz)

b. If the length of the fretboard is 40.0 cm, which of the string-note

combinations shown above can be played on an acoustic guitar? (Note

that the length of the string on a guitar is effectively reduced by pressing

the string on the appropriate fret on the fretboard.) (6 pts)

3. Some pieces may involve the use of open tuning which allows some chords

(combination of three or more notes) to be played just by keeping all strings

open. One example of open tuning is the repetitive open C tuning where the

strings (from 1st to 6th) are tuned to the following pitches:

G4 (392 Hz), E4 (330 Hz), C4 (262 Hz), G3 (196 Hz), E3 (165 Hz), C3 (131 Hz)

Calculate the wave velocity of each string in this case. (18 pts)

Answer 1

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