Using Resonance to Determine the Speed of Sound

AP Physics B Lab

The if you have ever plucked a guitar strings, or blown across the mouth of a pop bottle to create a tone, you have generated standing waves.  In general, a standing wave is one that oscillates with time, but remains fixed in its location.  It is in this sense that the way it is said to be standing. As one might expect, then, standing waves occur only if specific conditions are satisfied. 

            We begin by considering a string of length L that is tied down at both ends as in figure A.  If you plucked the string in the middle, it vibrates as shown in figure B..  This is referred to as the fundamental mode of vibration for this string, or also, as the first harmonic.  Clearly the string assumes a wave- like shape, but because of the boundary conditions, the ends tied down, the wave stays in place. As is clear from figure C, the fundamental corresponds to half a wavelength of the usual wave on a string.  One can think of the fundamental as being formed by this wave reflecting back and forth between the walls holding the string.  If the frequency is just right the reflections combine to give constructive interference and the fundamental is formed ; if the frequency differs from the fundamental frequency the reflections results in destructive interference and a standing wave does not result. We can find the frequency of the fundamental as follows:

 Where f is the fundamental frequency, v is the velocity of sound in the air and L is the length of the wave. The second, third, fourth, etc., frequencies can be found as follows:

In the same way that standing waves can be set up on a string, hollow tubes can also produce the same effect.  But there are two types of hollow tubes.  One type is that is open on one hand and closed on the other while the second is open at both ends.  Under these conditions, standing waves can be set up with displacement nodes and antinodes located in critical positions. 

Research constructive and destructive interference, resonance and standing waves and design a lab (Planning A and Planning B) to determine the speed of sound in air.

Materials available:

            hollow tubes, microphones, oscilloscopes, frequency generators (produce electronic signals (sine waves) at various frequencies), speakers, thermometers, sonic rangers, stopwatches, meter sticks, tuning forks. Inquire about any other equipment you may need.

The lab will be graded by the IB rubric given to all students.

The assignment is due on Friday, Jan9th, 2004.

The assignment will be graded as a lab and will count with a weight of one.

Students can collaborate on experimental methods and data gathering during lab time among members of their lab group but the report with analysis and conclusions must be of the students own work.