First get the speed of sound on that string:
speedsound=.73m/330 * 1/2 (half wavelength)
Then length from end for fret:
1/2* (.73-Length)=speedsoundabove/440
solve for length above.
Now, wavelength:
2(speedsoundabove)
speed sound at 20C: = 331.3 + (0.6 × 20) = 343.3 m/s
An unfingered guitar string is 0.73m long and is tuned to play E above middle C (330 Hz.) (a) How far from the end of this string must a fret (and your finger) be placed to play A above middle C (440 Hz)? (b) What is the wavelength on the string of this 440-Hz wave? (c) What are the frequency and wavelength of the sound wave produced in air at 20 Celsius by this fingered string?
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