(4) The frequency of vibrations of a vibrating violin string is given by 1 f = 2LV P where L is the length of the string, T is its tension, and p is its linear density. a) [6 pts] Find the rate of change of the frequency with respect to (i) the length (when T and p are constant), (ii) the tension (when L and p are constant), (iii) the linear density (when T and L are constant). b) [6 pts] 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. Determine what happens to the pitch of a note (i) when the effective length of a string is decreased by placing a finger on the I string so a shorter portion of the string vibrates, (ii) when the tension is increased by turning a tuning peg, (iii) when the linear density is increased by switching to another string