A string of linear density 1.5 g/m is under a tension of 20 N. What should be its length if its fundamental resonance frequency is 220 Hz?
A) 0.96 m
B) 0.26 m
C) 1.1 m
D) 1.2 m

Question

A string of linear density  1.5 g/m is under a tension of  20 N. What should be its length if its fundamental resonance frequency is  220 Hz?
A)  0.96 m
B)  0.26 m
C)  1.1 m
D)  1.2 m

Quizplus · Accepted Answer

The fundamental frequency of a string is given by $ f = \frac{1}{2L} \sqrt{\frac{T}{\mu}} $. Solving for L, $ L = \frac{1}{2f} \sqrt{\frac{T}{\mu}} $. Substituting $ f = 220 \, \text{Hz} $, $ T = 20 \, \text{N} $, and $ \mu = 1.5 \, \text{g/m} = 0.0015 \, \text{kg/m} $, we find $ L \approx 0.26 \, \text{m} $.

A String of Linear Density 1