The frequency of vibrations of a vibrating string is given

Last updated: 5/13/2023

The frequency of vibrations of a vibrating string is given by f 2L where L is the length of the string T is its tension and p is its linear density t a Find the rate of change of the frequency with respect to the following i the length when T and p are constant ii the tension when L and p are constant iii the linear density when L and T are constant b The pitch of a note how high or low the note sounds is determined by the frequency f The higher the frequency the higher the pitch Use the signs of the derivatives in part a to determine what i when the effective length of a string is decreased by placing a finger on the string so a shorter portion of the string vibrates df O and L is decreasing f is increasing higher note dL ii when the tension is increased by turning a tuning peg df dT V O and T is increasing f is increasing ili when the linear density is increased by switching to another string df dp 0 and p is increasing higher note fis decreasing lower note