A string A has double the length, double the tension, double the diameter and double the density than that of - Science - Sound

Question

A string A has double the length, double the tension, double the
diameter and double the density than that of string B Their
fundamental frequencies of vibration are nAand
nB, respectively

Jyoti Pant · Accepted Answer

We have a formula for fundamental frequency,
f=12lTm=12lTπD24×1×ρOr f=1lDTπρnB=1lDTπρnA=1(2l) (2D)2Tπ (2ρ)=14lDTπρSo,nA=14nBOr nB=4 nA

A string A has double the length, double the tension, double the diameter and double the density than that of string B. Their fundamental frequencies of vibration are nAand nB, respectively.

A string A has double the length, double the tension, double the diameter and double the density than that of string B. Their fundamental frequencies of vibration are n_Aand n_B, respectively.