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azamat
3 years ago
8

What are the first three overtones of a bassoon that has a fundamental frequency of 90.0 Hz? It is open at both ends. (The overt

ones of a real bassoon are more complex than this example, because its double reed makes it act more like a tube closed at one end.)
Physics
1 answer:
vekshin13 years ago
5 0

Answer:

f_{2}=180Hz,f_{3}=270Hz,f_{4}=360Hz\\

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

f_{1}=v/2L

The first overtone of bassoon is found by substituting n=2

So

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

The second overtone of bassoon is found by substituting n=3

So

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

The third overtone of bassoon is found by substituting n=4

So

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

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