Q. $n$ waves are produced on a string in one second. When the radius of the string is doubled and the tension is maintained the same, the number of waves produced in one second for the same harmonic will be
A) $\frac{n}{2}$
B) $\frac{n}{3}$
C) $2n$
D) $\frac{n}{\sqrt{2}}$
Explanation
(a) From $n = \frac{1}{lD}\sqrt{\frac{T}{\pi\rho}}$
When radius of string is doubled, Diameter $D$ becomes twice. As $T\ and\ \rho$ are same,$\ n\ becomes\frac{1}{2},\ ie,n/2$.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.