Speed of Sound using a Resonant tube

[baldbrain]

Homework Statement

In the experiment for the determination of the speed of sound using a resonance tube, the diameter of the column tube is 4 cm. The frequency of the tuning fork is 512 Hz. The air temperature is 38° C in which the speed of sound is 336 m/s. The zero of the meter scale coincides with the top end of the resonance column tube. When the first resonance occurs, the reading of the water level is
(a) 14.0 cm (b) 15.2 cm
(c) 6.4 cm (d) 17.6 cm
→ v=336 m/s, f=512 Hz, t=38° C, d=4 cm=0.04 m

Homework Equations

l₁+e=(1/4)(v/f)
where l₁ is the reading of the water level when the first resonance occurs, and e is the end correction.
Then, l₁+e=(1/4)(336/512)=0.1640625 m

The Attempt at a Solution

l₁+e=(1/4)(v/f)
where l₁ is the reading of the water level when the first resonance occurs, and e is the end correction.
Then, l₁+e=(1/4)(336/512)=0.1640625 m

How do I calculate the end correction in order to the water level?
How do I use the given temperature and the diameter of the tube?

 

[haruspex]

How do I calculate the end correction in order to the water level?

For each of the four options, what would the end correction have to be for that option?

 

[PeterO]

Homework Statement

In the experiment for the determination of the speed of sound using a resonance tube, the diameter of the column tube is 4 cm. The frequency of the tuning fork is 512 Hz. The air temperature is 38° C in which the speed of sound is 336 m/s. The zero of the meter scale coincides with the top end of the resonance column tube. When the first resonance occurs, the reading of the water level is
(a) 14.0 cm (b) 15.2 cm
(c) 6.4 cm (d) 17.6 cm
→ v=336 m/s, f=512 Hz, t=38° C, d=4 cm=0.04 m

Homework Equations

l₁+e=(1/4)(v/f)
where l₁ is the reading of the water level when the first resonance occurs, and e is the end correction.
Then, l₁+e=(1/4)(336/512)=0.1640625 m

The Attempt at a Solution

l₁+e=(1/4)(v/f)
where l₁ is the reading of the water level when the first resonance occurs, and e is the end correction.
Then, l₁+e=(1/4)(336/512)=0.1640625 m

How do I calculate the end correction in order to the water level?
How do I use the given temperature and the diameter of the tube?

When the pipe is round, there is a simple, common formula relating end correction with tube diameter.
Also, check that option (c) wasn't actually 16.4 cm rather than 6.4 cm.

 

[baldbrain]

For each of the four options, what would the end correction have to be for that option?

That's not supposed to be the way

 

[baldbrain]

When the pipe is round, there is a simple, common formula relating end correction with tube diameter.
Also, check that option (c) wasn't actually 16.4 cm rather than 6.4 cm.

Nope, it is 6.4 cm
And I don't have any such formula in this book

 

[baldbrain]

And what about the temperature?

 

[baldbrain]

When the pipe is round, there is a simple, common formula relating end correction with tube diameter.

I later checked Wikipedia and found that
e=0.3D, where D is the hydraulic diameter.
But we don't know if the given diameter is the hydraulic diameter.

 

[haruspex]

That's not supposed to be the way

Why not? You are assuming there is enough information to determine the reading, regardless of the options. Perhaps there is only enough information to rule out all except one of the options.

 

[PeterO]

Nope, it is 6.4 cm
And I don't have any such formula in this book

It would seem your book had no formula and the wrong figure for option (c) (or just a mis-print).

I expect the temperature is used as an explanation for why the speed was 336 m/s rather than 330 or any other commonly used value for the speed of sound.

As for the "hydraulic diameter", suppose you assume the given diameter IS the hydraulic diameter and see if the answer you get matches any of the provided answers.
It may help to draw yourself a diagram of the apparatus set-up.

How do you know Post 2 is not the way you are supposed to do it? At least use that as an exercise and see if anything looks interesting.

btw: what you have to do is recognise this as a multiple choice question - which means you are not only trying to find the answer; you are trying to identify which one of the provided answers is correct - often achieved by showing which of the provided answers are incorrect.

 

[andrevdh]

According to this source the end correction is 1/3 the diameter of the pipe
http://www.tutorvista.com/content/physics/physics-iii/waves/resonance.php

 

[PeterO]

According to this source the end correction is 1/3 the diameter of the pipe
http://www.tutorvista.com/content/physics/physics-iii/waves/resonance.php

Actually that reference says it is 0.3 x diameter, which is significantly different to 1/3 the diameter.

 

[baldbrain]

As for the "hydraulic diameter", suppose you assume the given diameter IS the hydraulic diameter and see if the answer you get matches any of the provided answers.

I am getting the answer assuming that,
15.20625 cm to be precise
So... thanks

 

[PeterO]

I am getting the answer assuming that,
15.20625 cm to be precise
So... thanks

btw: If you calculated the end correction for each example - assuming (c) was actually 16.4 - you would have found (a) 2.4 (b) 1.2 (c) 0.0 (d) -1.2 From that you should have seen that option (b) was the only viable one since 0.3 x 4 = 1.2,
(a) was there for those that added an end correction for each end - forgetting that only applies to an open pipe (open at both ends).
(c) - at 16.4 - was there for those who forgot about end correction altogether, or though it would be insignificant.
(d) was there for those who thought the pipe was further out of the water, rather than further into the water, due to end correction.
(b) was there for those who knew the correct answer.