Speed of Sound using a Resonant tube

In summary: Nope, it is 6.4 cmI later checked Wikipedia and found thate=0.3D, where D is the hydraulic diameter.But we don't know if the given diameter is the hydraulic diameter.
  • #1
baldbrain
236
21

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?
 
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  • #2
HPPAS said:
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?
 
  • #3
HPPAS said:

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.
 
  • #4
haruspex said:
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
 
  • #5
PeterO said:
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
 
  • #6
And what about the temperature?
 
  • #7
PeterO said:
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.
 
  • #8
HPPAS said:
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.
 
  • #9
HPPAS said:
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.
 
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  • #10
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
 
  • #11
andrevdh said:
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.
 
  • #12
PeterO said:
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
 
  • #13
HPPAS said:
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.
 
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1. What is a resonant tube?

A resonant tube is a cylindrical tube that is open on one end and closed on the other. It is used to measure the speed of sound by creating a standing wave within the tube.

2. How does a resonant tube measure the speed of sound?

The resonant tube measures the speed of sound by using a tuning fork or other sound source to produce a sound wave at a known frequency. The tube is then adjusted in length until the length of the tube matches a specific multiple of the wavelength of the sound wave. This creates a standing wave, and the length of the tube can be used to calculate the speed of sound.

3. What factors can affect the accuracy of a resonant tube measurement?

The accuracy of a resonant tube measurement can be affected by the temperature and humidity of the air inside the tube, as well as the accuracy of the tuning fork or sound source used. The diameter of the tube and the position of the open and closed ends can also affect the measurement.

4. How does the speed of sound vary with temperature and humidity?

The speed of sound increases with higher temperature and lower humidity. This is because sound travels faster in warmer and less dense air. Conversely, sound will travel slower in colder and more humid air.

5. Can a resonant tube be used to measure the speed of sound in different mediums?

Yes, a resonant tube can be used to measure the speed of sound in different mediums, as long as the sound source used is able to produce a sound wave in that medium. The length of the tube may need to be adjusted based on the properties of the medium, such as its density and temperature.

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