Question

The 3th overtone of one end fixed string produce a frequency of 72Hz and the
length between a node and the adjacent anti-node is 5cm.waht is:
(a) the length of the string ?
(b) the wave length in this overtone and in the 1st overtone?
(c) the wave speed ?
(d) the fundamental frequency?
(e) the longest wavelength?

Answer 1

a)

$$\frac{\lambda_3}{4}=5\ cm\to \lambda_3=20\ cm$$

$$L=\frac{3}{2}\lambda_3=\frac{3}{2}20=30\ cm.$$

b)

$$\lambda_3=20\ cm$$

$$\lambda_1=3\lambda_3=3\cdot 20=60\ cm$$

c)

$$v=f\lambda_3=(72)(0.2)=14.4\frac{m}{s}$$

d)

$$f_1=\frac{v}{2L}=\frac{14.4}{2(0.3)}=24\ Hz$$

e)

$$\lambda=\lambda_1=60\ cm.$$