A glass hydrometer of mass m floats in water of density p. The area of the neck of the hydrometer is A. The resonant frequancy for the vertical oscillations of the hydrometer is given by f = (1/2\pi) (Apg/m)^(1/2) Calculuate the fractional change in the resonant frequancy when the temprature changes from 20 to 30 degrees C. My effort: (2f\pi)^2 = Apg/m 2ln(2f\pi) = ln(Apg/m) 2ln(2) + 2ln(\pi) + 2ln(f) = ln(A) + ln(P) + ln(g) - ln(m) I tried to then differentiate but I got in a total kefuffel. In the question it gives the 'coefficient of linear expansion' for glass and the 'coefficient of volume expansion for water. Thanks in advance for any kind help you can offer. Best Regards, James.