A flute is designed so that it plays a frequency of 261.6 Hz, middle C, when all the holes are covered and the temperature is20.0 C.

(a) consider the flute to be a pipe open at both ends, andfind its length, assuming that the middle-C frequency is thefundametal frequency.

(b) A second player, nearby in a colder roomalso attempts to play middle C on an identical flute. A beatfrequency of 3.00 beats/s is heard. What is the temperatureof the room?

Our values are given as,

PART A) To get the speed of sound we use the equation

So the speed of sound at will be,

We know that for an open pipe the first harmonic or the fundamental mode will be

So the length of the flute will be

PART B) As the person in the colder room also attempts to play middle C the fundamental wavelength is unchanged so that,

So from the second player in the colder room the frequency will be

So the speed of sound in this room will be

So we get the temperature in the room from

Rearranging to find the temperature

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explanation: