You blow into a flute and make a perfect \"middle C\" note at 261.626 Hz. The sp

Question

You blow into a flute and make a perfect "middle C" note at 261.626 Hz. The speed of sounds at that temo is 342 m/s. Later, the room has warmed uo so the speed of sounds is now 346 m/s.

1. What is the frequency of the middle C at this high temperature?

2. What is the beat frequency if the two notes where played at the same time?

3. The flute can be lengthened or shorthened to change the tune. How far should the flute be lengthened or shortened in order for the flute to be in tune at the the hotter temperature?

Explanation / Answer

f = v/2L

Lis lenght of flute

f1 = 261.626 Hz, v1 =342 m/s , v2 =346 m/s

(1) f2/f1 =v2/v1

f2 = (346/342)(261.626)

f2 = 264.686 Hz

2) Beat frequency =f2-f1 = 264.686 -261.626

Beat frequency = 3.06 Hz

3) f= v/2L

f is same.

v2/v1 = L2/L1

L2/L1 = 346/342 = 4

L2 = 4L1

the length is increases to 4 times of initial value to tune at the hotter temperature

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