Question

The two strings in FIGURE P17.49 are of equal length and are being driven at equal frequencies. The linear density of the left string is 5.0 g/m. What is the linear density of the right string?

Short answer

The linear density of the right string is$\mu =\frac{9}{4}{\mu }_0$

Step-by-step solution

The concept of linear density 

Linear density is defined as the mass per unit length of a strand.

The key solution to the problem 

At first, the concept related to the difference between the same frequency is related to the same tension force. therefore, the provided equation of the frequency is $f_m=m\frac{v}{2L}=\frac{m}{2L}\sqrt{\frac{T}{\mu }}$

the following equality will be $\frac{2}{2L}\sqrt{\frac{T}{{\mu }_0}}=\frac{3}{2L}\sqrt{\frac{T}{{\mu }_{}}}$

Therefore, the simplification will be $\frac{2}{{\mu }_0}=\frac{3}{\mu }$

So the linear density will berole="math" localid="1649071992032" $\frac{\mu }{{\mu }_0}=\frac{3}{2}\Rightarrow \frac{\mu }{{\mu }_0}=\frac{9}{4}\Rightarrow \mu =\frac{9}{4}{\mu }_0$