An unfingered guitar string is 0.73m long and is tuned to play E above middle C (330Hz)?

a) How far from the end of this string must a fret (and yout 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 the wavelength of the sound produced in air at 20 C by this fingered string?





please when you answer these questions put in the formulaes you have used to obtain the result.

An unfingered guitar string is 0.73m long and is tuned to play E above middle C (330Hz)?
Use formula:





speed = frequency * wavelength





and knowledge that the note is the first harmonic of the length of the string:





wavelength = 2 * length





Let's calculate speed of the wave in your string:





v = 330 * 2 * 0.73 = 481.8 m/s





Now let's calculate length for the same speed and frequency 440 Hz:





l = 481.8 / (440 * 2) = 0.5475 m (ANSWER 1)





Wavelength on the string of this 440Hz wave is:





l = 2 * 0.5475 = 1.095 m (ANSWER 2)





For third question, we use the knowledge of the speed of the sound in air at 20 C





v = 343 m/s





As of the frequency, the string will make air vibrate with the same frequency as the string vibrates itself.





frequency = 440 Hz


wavelength = 343 / 440 = 0.7795 m (ANSWER 3)

jasmine