A wire of length 108 cm produces of fundamental note of 256Hz when stretched by a weight of 1kg. By how much its length should be increased so that its pitch is raissed by a major tone, if it is now stretched by a weight of 4kg?

Explanation

n=256Hz, Tension `=T =1 xx 9.8 =9.8N`
Length of the wire =l=108m
`n=1/(2l) sqrt(T/mu)`
`256=(1)/(2 xx 1.08) sqrt((9.8)/mu) ……..(i)`
where `mu` is the mass per unit length of the wire. When the pitch is raised by a major tone the frequency is `265 xx 9/8=288Hz`
New tension `=4 xx 9.8 =39.2N`
New length `=L=?`
`288=1/(2L) sqrt((39.2)/(mu)) ..........(ii)`
Dividing equation (ii) by (i) `(288)/(256)=(2 xx 1.08)/(2L) sqrt((39.2)/(mu)) xx mu/(9.8)`
`L=(1.08 xx 2 xx 256)/(288)=1.92m`
Increase in the length =1.92-1.08=0.84m