Consider a string in a guitar whose length is 80 cm and a mass of 0.32 g with tension 80 N is plucked . Compute the first four lowest frequencies produced when it is plucked .

Consider a string in a guitar whose length is 80 cm and a mass of 0.32

1.	Consider a string in a guitar whose length is 80 cm and a mass of 0.32 g with tension 80 N is plucked . Compute the first four lowest frequencies produced when it is plucked .
Answer» SOLUTION :The velocity of the wave , `v = SQRT((T)/(mu))` The length of the string , L = 80 cm = 0.8 m . The mass of the string , `m = 0.32` g = `0.32 xx 10^(-3)` KG Therefore , the linear mass DENSITY , `mu = (0.32 xx 10^(-3))/(0.8) = 0.4 xx 10^(-3) kg m^(-1)` The tension in the string , T = 80 N `v = sqrt((80)/(0.4 xx 10^(-3))) = 447.2 ms^(-1)` The wavelength corresponding to the fundamental frequency `f_(1)` is `lambda_(1) = 2 L = 2 xx 0.8 = 1.6` m The fundamental frequency `f_(1)` corresponding to the wavelength `lambda_(1)` `f_(1) = (v)/(lambda_(1)) = (447.2)/(1.6) = 279.5` Hz Similarly , the frequency corresponding to the second harmonics , third harmonics and fourthharmonics are `f_(2) = 2f_(1) = 559` Hz `f_(3) = 3f_(1) = 838.5`Hz `f_(4) = 4f_(1) = 1118` Hz