University Physics with Modern Physics (14th Edition)

(a) $f_1 = 156~Hz$ $\lambda_1 = 1.60~m$ (b) F = 467 N
(a) Let $f_1$ be the fundamental frequency. $n~f_1 = 624~Hz$, for some whole number $n$. $(n+1)~f_1 = 780~Hz$, for some whole number $n$. We can subtract the first equation from the second equation. $f_1 = 780~Hz-624~Hz = 156~Hz$ We can find the wavelength $\lambda_1$. $\lambda_1 = 2L$ $\lambda_1 = (2)(0.800~m)$ $\lambda_1 = 1.60~m$ (b) We can find the speed of the wave along the string. $v = f_1~\lambda_1$ $v = (156~Hz)(1.60~m)$ $v = 249.6~m/s$ We can find the tension $F$. $\sqrt{\frac{F}{\mu}} = v$ $F = v^2~\mu$ $F = (249.6~m/s)^2(0.00750~kg/m)$ $F = 467~N$