Question

A $160g$ rope $4m$ long is fixed at one end and tied to a light string of the same length at the other end. Its tension is $400N$. What are the wavelengths of the fundamental and the first two overtones?

• A. $16m,5.33m,3.2m$
  
• B. $18m,5.33m,3.2m$
  
• C. $18m,5.33m,3.7m$
  
• D. $18m,8.33m,3.2m$
  

Answer 1

The correct option is A $16m,5.33m,3.2m$

In such an arrangement, one fixed end acts as a node, and the other end attached to light string as antinode.

Thus in fundamental mode, $l=\frac{\lambda }{4}$

$⟹\lambda =4l=16m$

In first overtone, $l=\frac{3\lambda }{4}$

$⟹\lambda =5.33m$

In second overtone, $l=\frac{5\lambda }{4}$

$⟹\lambda =3.2m$