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

v = 45 Hz, mass per unit length `= 4.0 xx 10^(-2) kgm^(-1)`
Mass of the wire, `M = 3.5 xx 10^(-2)` kg
`m = ("Mass")/("Length")`
`4 xx 10^(-2) = (3.5 xx 10^(-2))/(l)`
length of wire, `l = (3.5 xx 10^(-2))/(4.0 xx 10^(-2)) = 0.875` m
Speed, `upsilon = ?, l = (lambda)/(2), lambda = 2l`
The speed of transverse wave `upsilon` = frequency `xx` wavelength
`= 45 xx 2 xx 0.875 = 78.75 ms^(-1)`
= 79 `ms^(-1)`
`upsilon = sqrt((T)/(m))`
Therefore, `T = upsilon^(2) xx m = (79)^(2) xx 4 xx 10^(-2)`
= 248 N