Question

1. A 6-cm-long guitar string is tuned to produce the note B3 (fundamental frequency 245 Hz). If the tension of the string is increase by 1%, what will be the change of the fundamental frequency of the string? a) 3.65Hz b) 4.85 Hz c) 2.44 Hz d) 1.22 Hz e) 5.34Hz

Answer 1

Answer:

Change in the fundamental frequency of the string is 1.22 Hz.

Explanation:

It is given that,

Length of string, l = 6 cm = 0.06 m

Fundamental frequency of the string, f = 245 Hz

If the tension of the string is increase by 1%, we need to find the fundamental frequency of the string. It is given by :

$f=\dfrac{1}{2l}\sqrt{\dfrac{T}{\mu}}$.............(1)

Where

T is the tension in the string

$\mu$ is mass per unit length

It is clear from equation (1) that the fundamental frequency is directly proportional to the tension in the string i.e.

$f\propto \sqrt{T}$

New tension, T' = 1.01 T

New frequency, $f'=f\times \sqrt{T}$

$f'=245\times \sqrt{1.01}$

f' = 246.22 Hz

So, change in the fundamental frequency is given by :

$\Delta f=f'-f$

$\Delta f=246.22-245$

$\Delta f=1.22\ Hz$

So, the change of the fundamental frequency of the string is 1.22 Hz. Hence, this is the required solution.