The 67.0-cm-long string of a guitar has a fundamental frequency of 314 Hz when i
ID: 1474889 • Letter: T
Question
The 67.0-cm-long string of a guitar has a fundamental frequency of 314 Hz when it vibrates freely along its entire length. A fret is provided for limiting vibration to just the lower two-thirds of the string. (a) If the string is pressed down at this fret and plucked, what is the new fundamental frequency? Hz (b) The guitarist can play a "natural harmonic" by gently touching the string at the location of this fret and plucking the string at about one-sixth of its length from the bridge. What frequency will be heard then? Hz
Explanation / Answer
Given,
Length = L = 67 cm = 0.67 m ; f = 314 Hz ;
we need to know the velocity of the sound wave in the string.
we know that, f = v/2L (v is the velocity of the wave)
v = f x 2L = 314 x 2 x 0.67 = 420.76 m/s
(a)Let f' be the new fundamental frequency.
As per the condition given:
L' = 2/3 L = 2/3 x 0.67 = 0.447 m
Again using, f = v / 2L
f' = v/2L' = 420.76 / 2 x 0.447 = 470.65 Hz
Hence, new fundamental frequency = f' = 470.65 Hz.
(b)The frequency that will be heard will be:
f'' = 2 f' = 2 x 470.65 = 941.3 Hz
Hence, f'' = 941.3 Hz.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.