Resonance and Determination of the Speed of Sound in Air

YSP summer 2014

Experiment 1

Resonance and determination of the speed of sound in air

This is an experiment to determine the speed of sound in air. We have a loudspeaker above a large empty graduated cylinder and will try to create resonance. The air column in the graduated cylinder can be adjusted by putting water in it. For each chosen frequency, the aim is to find a water column height for which a clear resonance is heard.

If the water level in the tube is gradually lowered from the top of the tube, resonance will occur when the position of the water level corresponds with the position of the first node. This position is sharply defined and may be accurately determined by listening for an extra intense sound. As the water level is further lowered, a second resonance point may be found that corresponds to the second node. In some cases additional nodes may be found, depending upon the relation between the wavelength and the tube length. The inter-nodal distance is just a half wavelength. We’ll adjust the water height finely to get the peak resonance and then carefully measure the length of the air column from the water surface to the top of the air column. The loudspeaker membrane is about 1cm above the top of the cylinder. Note that the frequency numbers in the table are for illustration only – should be replaced by numbers chosen in class.

(1)Fill out the last two columns in the table, assuming that

(a) the loudspeaker creates a displacement anti-node and the water creates a node, i.e. there is a displacement antinodeat d1cm above the open end of the tube and a displacement node at the water surface.

(b)the resonances correspond to the fundamental frequency (how can you make sure that this is the case?)

(c)assumptions (a) and (b) imply that L+d = /4

(2)every pair of (f,L) gives you a value for the speed of sound, using the relation v=f

(3)Take the average of your speed values and determine the uncertainty of your result for the speed of sound (std. deviation)

(4)Plot L (on y-axis) vs 1/f (on z-axis) and determine the slope of a linear trendline, using the fact that the slope = v/4. Compare the result from the slope with that from the average.

(5)Compare this experimental value of v with the theoretical value given (in m/sec) by: v (m/s) =331.5 + 0.61 Tc , where Tc is the temperature of the air in oC.

(6)Discuss the meaning of the intercept

(7)Explain the inherent errors in this experiment.

(8)Which of the values do you consider more reliable, the one from averaging or the one from the trendline? Explain.

(9)Report should have the usual parts, i.e. introduction, experimental apparatus and procedure of the experiment, data, analysis, uncertainties, summary, conclusion, as well as answers to the questions in the instructions.

(10)References:

(a)

(b)Crowell, Conceptual Physics chapter 8