Question

1.A string is 1.2m long.If the wave speed is 400m/s.Find the

a.first harmonic

b.second harmonic

c.third harmonic

d.fourth harmonic

e.tenth harmonic

2.Find the wavelength of each harmonic in problem 1.

a.first harmonic

b.second harmonic

c. third harmonic

d.fourth harmonic

e.tenth harmonic

Answer 1

1.

$$f_n=n\frac{v}{2L}$$

$f_1=\frac{400}{2*1.2}=167\:{\rm Hz},\quad f_2=2f_1=333\:{\rm Hz},\\ f_3=3f_1=500\:{\rm Hz},\quad f_4=4f_1=667\:{\rm Hz},\\ f_{10}=10f_1=1667\:{\rm Hz}$

2.

$$\lambda_n=\frac{2L}{n}$$

$\lambda_1=\frac{2*1.2}{1}=2.4\:{\rm m},\quad \lambda_2=\frac{2*1.2}{2}=1.2\:{\rm m},\\ \lambda_3=\frac{2*1.2}{3}=0.8\:{\rm m},\quad \lambda_4=\frac{2*1.2}{4}=0.6\:{\rm m},\\ \lambda_{10}=\frac{2*1.2}{10}=0.24\:{\rm m}$