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Sagot :
The frequency of the third harmonic if the pipe is closed at one end is = 102.93 Hz.
How can we find the frequency of the third harmonic if the pipe is closed at one end?
To find the frequency of the third harmonic if the pipe is closed at one end, we use the formula,
[tex]f_{n} =nf_{1}[/tex]=[tex]n\frac{v}{4L}[/tex] , in this case n= 1,3,5,7,9.....
Here we are given,
L= The length of the pipe = 4.137 m.
v= speed of the sound at 16.164°C .
[tex]v_{0}[/tex]= speed of the sound at 0°C.=331 m/s
Before finding the frequency we have to find the speed of the sound at 16.164°C. To find v, we are using the formula,
[tex]v=v_{0 } \sqrt{\frac{T_{2} }{T_{1} } }[/tex]=[tex]331\times \sqrt{\frac{(273+16.164) }{273 }[/tex]=340.65 m/s.
We have to find the frequency of the third harmonic, so according to the question, n=5
Now we put the known values in the first equation, we can find that
[tex]f_{n}=n\frac{v}{4L}[/tex]
Or,[tex]f_{n} = 5\times\frac{340.65}{4\times 4.137}[/tex]=102.93 Hz.
Therefore, from the above calculation we can conclude that if the pipe is closed at one end the frequency of the third harmonic is 102.93 Hz.
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