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In a pipe closed at one end and filled with air, a 384-Hz tuning fork resonates when the pipe is 22-cm-long; this tuning fork
does not resonate for any smaller pipes.
(a) State three other lengths at which this pipe will resonate with the 384-Hz tuning fork. Explain / show your
reasoning​

Respuesta :

Answer:

Three other length for which resonance will occur is 66 cm, 110 cm and 154 cm

Explanation:

As we know that the length of the pipe is 22 cm

Now let say it is in 1st harmonic state so we have

[tex]\frac{\lambda}{4} = L[/tex]

so we have

[tex]\frac{\lambda}{2} = 2L[/tex]

So we have

[tex]L_1 = L + \frac{\lambda}{2}[/tex]

[tex]L_1 = L + 2L[/tex]

[tex]L_1 = 22 + 2L[/tex]

For N = 1

[tex]L_1 = 66 cm[/tex]

For N = 2

[tex]L_2 = 22 + 88[/tex]

[tex]L_2 = 110 cm[/tex]

For N = 3

[tex]L_3 = 22 + 132[/tex]

[tex]L_3 = 154 cm[/tex]