Answer:
[tex]f_{2}=180Hz,f_{3}=270Hz,f_{4}=360Hz\\[/tex]
Explanation:
Given data
Frequency f=90 Hz
To find
First three overtones of bassoon
Solution
The fundamental frequency of bassoon is found by substituting n=1 in below equation
f=v/λ=nv/2L
[tex]f_{1}=v/2L[/tex]
The first overtone of bassoon is found by substituting n=2
So
[tex]f_{2}=2v/2L\\f_{2}=2(v/2L)\\as \\f_{1}=v/2L\\So\\f_{2}=2f_{1}\\f_{2}=2(90Hz)\\f_{2}=180Hz[/tex]
The second overtone of bassoon is found by substituting n=3
So
[tex]f_{3}=3v/2L\\f_{3}=3(v/2L)\\as \\f_{1}=v/2L\\So\\f_{3}=3f_{1}\\f_{3}=3(90Hz)\\f_{3}=270Hz[/tex]
The third overtone of bassoon is found by substituting n=4
So
[tex]f_{4}=4v/2L\\f_{4}=4(v/2L)\\as \\f_{1}=v/2L\\So\\f_{4}=4f_{1}\\f_{4}=4(90Hz)\\f_{4}=360Hz[/tex]
