A wire stretched between two rigid supports vibrates in its fundamental mode with a frequency of 45Hz. The mass of the wire is `3.5xx10^(-2)`kg and its linear mass density is `4.0xx10^(-2)kgm^(-1)`. What is (a) the speed of a transverse wave on the string , and (b) the tension in the string?

Explanation

Frequency of fundamental mode, `v=45Hz` Mass of wire M`=3.5**10^(-2)kg`,mass per unit length, m=`4.0**10^(-2)kgm^(-1)`
`therefore Length of wire L=M/m= `(3.5**10^(-2))/(4.0**10^(-2))=0.875m`. (a) For fundamental mode `L= lambda/2or lambda = 2L=0.875**2=1.75m`
`therefore velocity v = vlambda=45**1.75=78.75ms^(-1)`.
(b)The velocity of transverse wave `v=sqrt(T/m) RightarrowT= v^(2)m=(78.75)^(2)**(4.0)**10^(2)=248.6N`.