Plucking a guitar string creates standing waves, which oscillate with a xed freq
ID: 1554633 • Letter: P
Question
Plucking a guitar string creates standing waves, which oscillate with a xed frequency. Imagine that you pluck the Low E string on a guitar, which has a length of L = 0.67 m. The waves in this string travel with a speed of vstring = 110 m/s. (a) What frequency of sound do you produce when you pluck the Low E string? (b) Where should you press your nger on the string to produce a note that is one octave above the note in part (a)? What is the frequency of this note? (c) If the note you pluck in part (a) produces sound with a wavelength of 4.26 m, what is the speed of sound in the room where you are playing?
Explanation / Answer
a)
For standing wave we have relation,
F=v/2L
Plugging given data,
F=110/(2*0.67) = 82.09 Hz
b)
Now F’=F*8 = 82.09*8=656.72 Hz
Again
F’=v/(2L’)
656.72 =110/(2*L’)
L’=(110/656.72)/2 = 0.335m
c)
v=F*=82.09*4.26 = 349.7 m/s