Question

Calculate the frequency of the 3rd normal mode of a guitar string of length 40.0cm and mass 0.5g when stretched with a tension of 80N

Answer 1

Solution :-

Since the string is vibrating in $3^{rd}$ fundamental mode, frequency(ν) is given by:-

$\boxed{\nu =\frac{3v}{2L}}-----(1)$

v: wave velocity

L: length of string =0.4m

Wave velocity in a string is given by relation :

$v=\sqrt{\frac{T}{\mu}}$ μ: linear mass density i.e $\mu=\frac{M}{L}$

$v=\sqrt{\frac{80(0.4)}{(0.5)}}\\\\=>v=\sqrt{64}}\\\\=>\boxed{v=8ms^{-1}}----(2)$

From (1) and (2);

$=>\nu =\frac{3(8)}{2(0.4)}\\\\=>\boxed{\boxed{\nu= 30Hz}}$

Hope this answer helped you :)