Fundamental frequency

Question

The fundamental frequency of a guitar string is 384 Hz.

What is the fundamental frequency if the tension in the string is reduced by half?

Answer 1

Tension is proportional to the square of the frequency. Therefore, if the tension is reduced by 1/2, the frequency is reduced by the square root of two ( a factor of about 1.4 ).

Answer 2

Question:

fundamental frequency

The fundamental frequency of a guitar string is 384 Hz.

What is the fundamental frequency if the tension in the string is reduced by half?

Answer:

Formula: F=(1/L) SQRT(T/mu), where

F=Fundamental Frequency; fo original & fn new

L=Length of string (constant)

T=Tension; to original & tn new

mu=Mass per unit length (constant)

But that formula can be rearranged to be

T=4L^2 * F^2 * mu    and problem stated that    to=2 * tn

therefore,

4L^2 * fo^2 * mu = 2* (4L^2 * fn^2 * mu)

4L^2 * (384)^2 * mu = 8L^2 * fn^2 * mu   .  .  .  substitute

(384)^2 = 2 * fn^2  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  reduce

fn = 384 / sqrt (2)   .  .  .  .  .  .  .  .  unknown alone

fn = 271.529 Hz  .  .  .  .  .  .  .  .  .  Using a calculator