The top string of a guitar has a fundamental frequency of 33O Hz when it is allowed to vibrate as a whole, along all its 64.0-cm length from the neck

Burhan Hopper

Burhan Hopper

Answered question

2021-02-26

A guitar's top string's fundamental frequency is 330 Hz when it is allowed to vibrate as a whole, along all its 64.0-cm length from the neck to the bridge. A fret is provided for limiting vibration to just the lower two thirds of the string, What is the new fundamental frequency if the string is pulled while being squeezed down at this fret? 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 the way along its length from the bridge. What frequency will be heard then?

Answer & Explanation

Lacey-May Snyder

Lacey-May Snyder

Skilled2021-02-28Added 88 answers

As the string is vibrating in its fundamental frequency
L=λ2
λ=2L=20.64m=1.28m
The speed of the wave in the string is
V=fλ=3301.28=422Hz
a) If the string is stopped by a fret then
L = (2/3)0.64
so (23)0.64=λ2
λ=0.853m
frequency f1=Vλ
= 422Hz / 0.853 = 495 Hz
b) When plucking the string at one sixth the way of the lengthof the string
2L=3λ ( the string vibrates with third resonance Possibility)
λ=0.4266m
frequency f2=4220.27m=990Hz.

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?