Answer:
The fundamental frequency and the length of the pipe are 115.8 Hz and 1.48 m.
Explanation:
Given that,
First frequency = 986 Hz
Second frequency = 1102 Hz
We need to calculate the length of the pipe
Using formula of length
[tex]\Delta f=f_{2}-f_{1}=\dfrac{nv}{2L}[/tex]
Put the value into the formula
[tex]1102-986=\dfrac{1\times343}{2\times L}[/tex]
[tex]L=\dfrac{343}{2\times116}[/tex]
[tex]L=1.48\ m[/tex]
We need to calculate the fundamental frequency of this pipe
[tex]f_{1}=\dfrac{nv}{2L}[/tex]
Put the value into the formula
[tex]f_{1}=\dfrac{1\times343}{2\times1.48}[/tex]
[tex]f_{1}=115.8\ Hz[/tex]
Hence, The fundamental frequency and the length of the pipe are 115.8 Hz and 1.48 m.