Question

Problem 28a

Answer 1

Given information

Given :- The frequency of the vibrating violin string is given by, 

To find :-  (a) Find the rate of change of frequency with respect to 

 (i) the length (where    and  are constant ), 

 (ii) the tension ( where    and  constant ), and 

 (iii) the linear density (where  and  are constant ). 

Step-by-step explanation

Step 1.

(i) Finding the derivate w.r.t  using the power rule , 

  

(ii) Finding the derivate w.r.t.  using the chain rule,

  

  

(iii) Finding the derivative w.r.t. to  using chain rule,