Final answer:
To find the rate of change of the frequency with respect to different variables, differentiate the formula f = 1/2L √T/P. The rates of change are df/dL = -1/2L^2 √T/P, df/dT = 1/2L √1/T∙P, and df/dP = -1/2L √T/P^2.
Step-by-step explanation:
To find the rate of change of the frequency with respect to:
a) the length (when T and P are constant), differentiate the formula f = 1/2L √T/P with respect to L. The rate of change is given by df/dL = -1/2L^2 √T/P.
b) the tension (when L and P are constant), differentiate the formula f = 1/2L √T/P with respect to T. The rate of change is given by df/dT = 1/2L √1/T∙P.
c) the linear density (when L and T are constant), differentiate the formula f= 1/2L √T/P with respect to P. The rate of change is given by df/dP = -1/2L √T/P^2.