Constants part a flutist assembles her flute in a room where...

Part A A flutist assembles her flute in a room where the speed of sound is 342 m/s. When she plays the note A, it is in perfect tune with a 440 Hz tuning fork. After a few minutes, the air inside her flute has warmed to where the speed of sound is 346 m/s. How many beats per second will she hear if she now plays the note A as the tuning fork is sounded? Beats: _______ Part B How far does she need to extend the "tuning joint" of her flute to be in tune with the tuning fork?

Transcript

00:01 In this problem, you're considering someone playing the flute.

00:06 We're told that when the speed of sound is 342 meters per second, that the frequency of the flute matches the frequency 440 hertz.

00:24 But that later, the speed of sound increases to 300, 46 meters per second and in this case we want to know what is the frequency of beats that will be heard by our person playing the flute so in order to figure out the frequency of beats we need to figure out what will be the frequency played by the flute with this new speed of sound so the frequency f2 is going to be equal to speed of sound v2 over wavelength lambda by the speed of sound equation.

01:10 And the wavelength shouldn't change.

01:13 The wavelength is going to depend on the properties of the string.

01:17 So the length and mass of the string.

01:20 So it will not change, even though the speed of sound changes.

01:24 And so we can figure out what lambda is using the initial information given.

01:30 Again, using the speed of sound equation, lambda will be v1 over f1.

01:37 So we can go ahead and plug that in, and we get that the frequency played by our flute with the new speed of sound is going to be about 445 hertz with rounding.

01:56 So then the frequency of the beats will be equal to the.

02:03 Absolute value of the difference between them, which the difference between 440 and 445 is 5 hertz.

02:12 So our flute player will hear beats, we'll hear 5 beats every second...

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