The Resonance Tube

THE RESONANCE TUBE

AIM

1.To determine the velocity of sound in air, at room temperature, by means of a resonance tube.

2.To establish that resonance occurs in the tube, at a certain frequency, only when the tube has particular fixed lengths.

Questions, identified by a letter e.g. (a) are referred to as you read these notes. They are listed at the end. Answer them as you read.

APPARATUS

Tall glass measuring cylinder, length of glass tubing of approx. internal diameter of 40 mm, stand and clamp for tube, series of tuning forks of differing frequency and a large rubber stopper.

THEORY

For all forms of wave motion v = f  , where v is velocity, f is frequency and  is wavelength.

The air inside the tube will resonate in much the same fashion as air inside an organ pipe, that is when standing waves can be set up so that a pressure antinode occurs at the closed end of the tube while a pressure node occurs at the open end of the tube.

The diagram at right shows the simplest standing wave that can be set up in the resonating tube, this frequency which causes such a standing wave is called the FUNDAMENTAL or 1st HARMONIC and always occurs for the shortest length of tube which produces resonance. (a) (b) (c)

At resonance, the length of the tube is related to the wavelength of the standing wave set up in the air inside the tube and since the resonant frequency and wavelength are related to the velocity of sound in the air, the speed of sound in air can be determined. (d) (e) (f)

METHOD

1.Partly fill the tall cylinder with tap water and stand the tube upright in it. Be careful not to break either through carelessness. Arrange a stand with a clamp so that the tube can be clamped in any vertical position.

2.Excite the tuning fork by striking it on the palm of the hand or by striking it half-way down the prong on the rubber stopper. Do NOT hit the tuning fork on the bench top or with any hard object as this will permanently damage it and alter its frequency.

3.Hold the end of the prongs about 5 cm away from the open end of the tube and carefully listen for resonance while gradually increasing the length of the air column in the tube. When the air in the tube is in resonance with the tuning fork, carefully clamp the tube in position and measure the length of the tube protruding above the water meniscus to the nearest millimetre. Repeat the procedure, using the same frequency to excite the tube, at least two more times. Record these lengths, average length and exciting frequency in tabular form as shown overleaf.

4.Repeat procedures 2 and 3 for at least another four different exciting frequencies and record as before.

5.Plot a graph of average length, l, versus frequency, f. Draw in error bars to reflect the range of lengths measured (g) (h)

6.Plot a graph of average length, l, versus a suitable function of frequency that will produce a straight line graph. Note: The line may not go through the origin. (i)

7.Calculate from this graph the average velocity of sound in air, at the temperature of the experiment, giving an estimation of the uncertainty of your value and compare with the velocity of sound in your text book. (j)

8.Obtain a tube of identical internal radius to that used in 1 to 7 above, but longer. Using a tuning fork of intermediate frequency (e.g. 384 Hz) obtain resonance for two different lengths of the tube. Comment. (k)

Name: ......

THE RESONANCE TUBE

QUESTIONS

(a)Explain what is meant by the term "resonance". Explain in qualitative terms why a pressure antinode occurs at the closed end of the tube and a pressure node occurs close to the open end of the tube.

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(b)What approximate relationship holds between the length of the tube and the wavelength of the standing wave for this fundamental mode of vibration?

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(c)Write down the relationship that exists between V, f, and l.

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(d)What shape of graph should be obtained if wavelength,  is plotted versus frequency, f?

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(e)What shape of graph would be obtained if tube length, l, is plotted versus frequency, f?

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(f)What function of frequency, f, should be plotted against tube length, l, to obtain a straight line graph?

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How is the gradient of this graph related to the velocity of sound, V ?

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(g)Does the shape of your graph of tube length versus frequency agree with your answer to (e)?

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(h)To obtain a straight line graph, what values should you now enter into the last column of your results table?

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(i)Measure the gradient of this second graph. Include units.

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(j)Use your gradient and your answer to (f) to obtain a value for the speed of sound in air. Include units

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(k)You can obtain resonance at two different lengths using the same tuning fork – why? Draw the standing wave patterns set up in these two different lengths from the point of view of pressure amplitude. The mode of vibration set up in the longer length air column is called the first "overtone".

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What is the approximate relation between the tube length and the wavelength of this first "overtone"?

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Resonance Prac Marking Scheme

g)No marks

h)1 mark1/f or 1/l

i)3 marks2 for value, 1 for units

j)3 marks2 for value, 1 for units

k)7 marks2 for explanation of different amounts of the standing wave in the air column

1 mark for fundamental mode

2 marks for 1st overtone

2 marks for relationship l = ¾ 

Graphs3 marks each Correct plotting (check this) correct labels and units