Question

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?

Answer 1

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