Question

A wire 8.0 m long has a mass of 94 g, which is stretched under a tension of 450 N. List (in order from smallest to largest) the three lowest harmonic frequencies that can form on this string,

a.) if the ends of the string are both fixed.
Hz, Hz, Hz

b.) if one end is fixed and the other is free.
Hz, Hz, Hz

Answer 1

$$v=\sqrt{\frac{Tl}{m}}$$

$$v=\sqrt{\frac{(450)(8)}{0.094}}=196\frac{m}{s}$$

a)

$$f=\frac{nv}{2L}$$

$$f_1=\frac{(196)}{2(8)}=12.25\ Hz$$

$$f_2=\frac{2(196)}{2(8)}=24.5\ Hz$$

$$f_3=\frac{3(196)}{2(8)}=36.75\ Hz$$

b)

$$f_1=\frac{(196)}{4(8)}=6.125\ Hz$$

$$f_2=\frac{3(196)}{4(8)}=18.375\ Hz$$

$$f_3=\frac{5(196)}{4(8)}=30.625\ Hz$$