Question

One peculiar component of musicians’ contracts is that the temperature of concert halls must be maintained very precisely. The reason for this is that the pitch of the notes they play can change and thus make them sound bad. There two phenomena that contribute to this: on the one hand the speed of sound varies with temperature; on the other hand, the length of their instrument’s changes too. Let’s examine which effect is more important.

Assume that a marching band musicians plays the note C₄ (261.63 Hz- this is the fundamental frequency so n=1) on the flute (a pipe with two open ends) made of silver in Cleveland on a cool day with temperature of 5 ^oC for which the speed of sound is 334m/s . The band flies to New Mexico, where the temperature on the next day is 35^oC corresponding to the speed of the sound that is 352m/s.

1. Ignore thermal expansion. Compute the fundamental frequency that is produced when the musician tries to play that same note by accounting for the change of the speed of sound. (Length of tube remains the same).
2. Ignore the change of the speed of sound. Compute the linear thermal expansion of the flute, and from that the new frequency of the note. (Length changes but speed of sound doesn’t)

Answer 1