Answer to Question #96391 in Atomic and Nuclear Physics for Abdul Karim Saad

Question

The following sets of readings are for a hypothetical Resonance Tube Experiment.The Frequency of the turning forks is f and l is the first resonant length


F(Hz) 200 250 300 350 400 450
l(cm) 33.5 24.0 18.3 14.3 11.3 8.9
1. Obtain an equation for l in terms of f
2. Plot a graph with l as ordinate and f-1( F Whole Number,Raise to de power negative 1(-1) )
3. Use the graph to determine the speed of sound in air and the end correction of the tube

Answer 1

1) The equation for the speed of the wave is:

$$v=\lambda f=4(l+0.3d)\cdot f,\\ \space\\ l=\frac{v}{4f}-0.3d.$$

2) Plot l(1/f):

So the equation can be written as

$$l=\bigg(\frac{8801.5}{f}-10.827\bigg)\text{ cm}.$$

Or:

$$l=\bigg(\frac{35206}{4f}-0.3\cdot36.09\bigg)\text{ cm}.$$

and the speed of sound is 35206 cm/s, or 352,06 m/s.

3) That is the tube which is open at one end and closed at the other, because the wavelength is four times resonance length.