In resonance tube experiment if V=300 m/s, n=500 Hz, L= 125 cm. Find the maximum order of resonance that can be established. Maximum number of resonance and Maximum and minimum water level kept at resonance condition.

Question

abhisar · Answer

@Vincent-Lyon.Fr

abhisar · Answer

@IrishBoy123 @Michele_Laino @ParthKohli

ganeshie8 · Answer

$\lambda = v/f = 300/500 = 60cm$

First time resonace occurs at a air column height of $\lambda/4 = 15cm$. Therefore the maximum water level at which resonance occurs is $125-15 = 110cm$.

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ganeshie8 · Answer

subsequent air column heights at which resonance occurs are given by  $60/4 + n*60/2$, $n\in \mathbb{N}$

abhisar · Answer

@ganeshie8 yes I figured it out.

For the first question,

$$\frac{ 300 }{ 500 \times 4 }\times (2n-1)=1.25 \ \Rightarrow n=4.66$$

So maximum number of resonance will be 4 only.

abhisar · Answer

Do you have any Idea what does maximum order of resonance means?

ganeshie8 · Answer

@IrishBoy123 @Michele_Laino

michele_laino · Answer

here is my reasoning:
we are able to hear sounds from one sound tube, since the supplied air will undergo  the resonance condition, so we have two cases.

1) case of tube with one closed end
the emitted frequency are:
$${\nu _n} = \left( {2n + 1} \right){\nu _0},\quad n = 1,\;2,\;3,...$$
and $\nu_0$ is the fundamental frequency:
$${\nu _0} = \frac{{{v_S}}}{{4L}}$$
where $L$ is the length of the sound tube, and $v_S$ is the sound speed
so, the maximum number of resonance, is the closest integer such that:
$$2n + 1 \leqslant \frac{{{\nu _E}}}{{{\nu _0}}}$$
where $\nu_E$ is the emitted frequency, by the sound tube.

2) similarly, if we have an opend sound tube, we have the corresponding formulas:
$$\begin{gathered}
  {\nu _n} = \left( {n + 1} \right){\nu _0},\quad n = 1,\;2,\;3,... \hfill \
  {\nu _0} = \frac{{{v_S}}}{{2L}} \hfill \ 
\end{gathered} $$
and the maximum number of resonance, is the closest integer, such that the subsequent condition holds:
$$n + 1 \leqslant \frac{{{\nu _E}}}{{{\nu _0}}}$$

michele_laino · Answer

oops.. I meant 
2) ...a sound tube with opened ends...

michele_laino · Answer

of course, ${{\nu _E}}$ is the $maximum$ emitted frequency, by the sound tube, in both cases

vincent-lyon.fr · Answer

There are 4 possible resonances in the tube.

Is the answer supposed to be 4, or to be 7?

abhisar · Answer

Thanks @ganeshie8 and @Michele_Laino . That was a very thorough explanation!

But I am still confused about "Maximum order of resonance". I don't know what does it mean?

@Vincent-Lyon.Fr , yes the maximum number of resonance is supposed to be 4. Can you help me understand  "Maximum order of resonance". Thanks

ganeshie8 · Answer

Is there any definition/formula kindof thing about  "Maximum order of resonance" in your textbook ?

ganeshie8 · Answer

I have googled a bit, but didn't get any satisficatory results

vincent-lyon.fr · Answer

I have never heard that term before. 
I would have worded the question this way:
"How many resonances can be obtained when running the experiment?"

abhisar · Answer

No I don't have any definition about that in my textbook. It's just a random question from practice sets. The answer to "Maximum order of resonance" for this question is also given 4. So I think by this they mean Maximum number of resonances.