Answer
a) $f_{G2}=784Hz$
$f_{G3}=1176Hz$
$f_{B2}=988Hz$
$f_{B3}=1482Hz$
b) $\frac{m_B}{m_G}=1.59$
c) $\frac{l_G}{l_B}=1.26$
d) $\frac{F_{TG}}{F_{TB}}=0.630$
Work Step by Step
a) $f_n=nf_1$
$f_{G2}=2\times392Hz=784Hz$
$f_{G3}=3\times392Hz=1176Hz$
$f_{B2}=2\times494Hz=988Hz$
$f_{B3}=3\times494Hz=1482Hz$
b) $v=\sqrt{\frac{F_Tl}{m}}=2lf_1$
$m=\frac{F_Tl}{v^2}$
$\frac{m_G}{m_B}=\frac{v^2_B}{v^2_G}=\frac{(2l(494Hz))^2}{(2l(392Hz))^2}=1.59$
c) $F_T=\mu v^2=\mu (2lf_1)^2$
$(2l_Gf_{G1})^2=(2l_Bf_{B1})^2$
$\frac{l_G}{l_B}=\frac{f_{B1}}{l_{G1}}=\frac{494Hz}{392Hz}=1.26$
d) $\frac{F_{TG}}{F_{TB}}=\frac{v_G^2}{v_B^2}=\frac{1}{1.59}=0.630$
