Answer to Question #97958 in Classical Mechanics for Surej

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)

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