One closed organ pipe has a length of 2.24 meters. When a second pipe is played at the same time, a beat note with a frequency of 1.1 hertz is heard. By how much is the second pipe too long? Include units in your answer.

Respuesta :

ANSWER

0.07 m

EXPLANATION

First, we have to find the frequency that the first pipe would play,

[tex]\lambda=4L=4\cdot2.24m=8.96m[/tex]

The frequency is,

[tex]f=\frac{v}{\lambda}=\frac{343m/s}{8.96m}=38.28125Hz[/tex]

The frequency played by the second pipe is,

[tex]f=38.25125Hz-1.1Hz=37.18125Hz[/tex]

The wavelength of this note is,

[tex]\lambda=\frac{v}{f}=\frac{343m/s}{37.18125s^{-1}}\approx9.2251m[/tex]

So the length of the second pipe is,

[tex]L=\frac{\lambda}{4}=\frac{9.2251m}{4}\approx2.31m[/tex]

The difference between the pipes' length is,

[tex]2.31m-2.24m=0.07m[/tex]

Hence, the second pipe is 0.07 meters too long