For sound waves travelling in dry air at normal pressure the speed v varies with Celsius temperature θ according to the empirical relation v=331+0.6θms−1. A tuning fork of frequency 1024Hz is sounded successively in air at 0∘C and then in air at 30∘C.
a. (i) Derive an expression for the wavelength λ of the sound in air as a function of the temperature θ, keeping the frequency constant.
b. (ii) Using the expression obtained in (i), calculate the wavelength at 0∘C and at 30∘C.
c. (iii) Find the fractional change in wavelength per degree Celsius between these two temperatures.
d. (iv) Comment on the practical significance of this temperature dependence for precise acoustic measurements.