A whistle is constructed so that it behaves as an air column closed at one end and open at the other. The whistle is intended to sound a note of 512\,Hz when blown, and it is designed to operate in its third resonant mode. Assume end corrections can be neglected.
(a) Determine the required physical length of the whistle if the speed of sound in air is 344\,m\,s−1. Show all calculations clearly.
(b) On a cold day the speed of sound falls to 330\,m\,s−1 while the length of the whistle remains unchanged. Calculate the new frequency of the whistle when it is operated in the same resonant mode.
(c) Compute the percentage change in frequency caused by the temperature drop. Discuss briefly how the pitch perceived by a listener would change as a result.