Two identical strings X and Z made of same material have tension T_{X} and T_{Z} in then If their fundamental frequencies are 450 Hz and 300 Hz, respectively, then the ratio T_{X}/T_{Z} is :

(1) 1.25

(2) 0.44

(3) 1.4

(4) 2.25

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Ans. (4) 2.25

Sol. $f_x={1\over2l}\sqrt{T_x\over\mu}$

$f_z={1\over2l}\sqrt{T_z\over\mu}$

${f_x\over f_z}={450\over300}=\sqrt{T_x\over T_z}$

$\implies T_x/T_z = 9/4 = 2.25$

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