The frequency of vibrations of a vibrating string (in Hertz) is given by
f = 1/(2L) * sqrt(T/rho),
where L is the length of the string (in meters), T is the tension in the string (in Newtons) and rho is the linear density of the string (in kg/m).
(a) Write down an expression for the rate of change of frequency with respect to
i. length (T and rho are constant)
ii. linear density (T and L are constant)
iii. tension (L and rho are constant)
Include appropriate units.
(b) The pitch of a note is determined by its frequency (higher the frequency, higher the pitch). What happens to the pitch of the note if
i. the tension in the string is increased, keeping L and rho constant.
ii. linear density of the string is increased, keeping L and T constant.
