Fundamental frequency of a sonometer wire increases by SHM If its tension is increased by 21% How will frequency be - Physics - Waves

Question

Fundamental frequency of a sonometer wire increases by SHM If
its tension is increased by 21% How will frequency be affected if
its length is increased by 10% Please give the method (ans=45
45Hz)

Kranav Sharma · Accepted Answer

The fundamental frequency of a sonometer wire is expressed
as
f = (1/ 2L) ( T/ m )1/2
here
T = tension in the string
m = mass per unit length of string
L = length of the string
now, if
tension is increased by 21%
T' = T + 0 21T = 1 21T
length is increased by 10%
L' = L + 0 1L = 1 1L
and as mass per unit length remains constant
thus, fundamental frequency becomes
f' = (1/ 2L') ( T'/ m )1/2
= (1/ 2 x 1 1L) ( 1 21T/ m )1/2
= (1 1 / 1 1) (1/ 2L) ( T/ m )1/2
thus
f' = f
thus, the fundamental frequency does not change

Fundamental frequency of a sonometer wire increases by SHM.If its tension is increased by 21%.How will frequency be affected if its length is increased by 10%.Please give the method. (ans=45.45Hz).