This manual describes the laboratory experiment used during the 1996 - 1997 academic year. Significant changes have been made since then, and the manual used during the current academic year is in NOT available yet on the WEB. Hardcopies can be purchased at the bookstore.
To determine the speed of sound in air and in metal.
Recall our knowledge of standing waves established in a stretched string which is fixed at both ends. A wave traveling down the length of the string is reflected at the end and returns in the opposite direction (with the same wavelength). If the length of the string is chosen such that the superposition of these two waves establishes a pattern of standing waves, we call this condition resonance.
Likewise, standing sound waves can be achieved in a tube with either one or both ends open. As with the stretched string, resonance is established if the length of the tube is chosen appropriately according to the wavelength (or frequency) of the sound waves. The open end of the tube corresponds to the location of a displacement antinode, i.e., where the amplitude of the oscillations is at its maximum value. The closed end of the tube corresponds a displacement node, i.e., where the amplitude of the oscillations is zero.
The fundamental harmonic corresponds to the lowest frequency at which standing waves are established. The second harmonic is the next highest frequency resulting in standing waves. The same applies for higher order harmonics.
As we know, the speed (v), the frequency (f), and the wavelength ([[lambda]]) are related by
v = [[lambda]] f (11.1)
Thus, if we can determine the wavelength ([[lambda]]) of sound within a tube and its frequency (f), then we can easily determine the speed of sound (v).
The following homework must be finished prior to class and should be turned in to the lab TA before the start of the lab. Also, please read the instructions for this lab.
Longitudinal vibrations produced by a tuning fork are transmitted through the air into a plastic tube with an adjustable piston at one end (see the Figure 11.1). By suitably adjusting the length of the air column using the piston, standing waves are produced in it. The locations of the nodes of the standing waves are determined by the lengths of the air column required to produce resonance. By knowing the distance between the nodes, the wavelength of the vibration can be found. Since the frequency of the tuning fork is given (it is stamped on the side of the fork), the speed of sound in the air can be calculated.
Let be the frequency of vibrations of the tuning fork. This will also be the frequency of the tone in the air column. If is the wavelength of the sound in air, then the speed of sound in air is just,
To determine the speed of sound in a metal rod, we will use a procedure known as Kunzt's method. Longitudinal vibrations, produced in a uniform metal rod clamped at its center, are transmitted to the air inside a tube closed at one end (see Figure 11.2). By adjusting the effective length of the air column, standing waves are produced. The presence of the standing waves is determined in this case by placing some light powder or dust in the tube. The vibration of the air causes the dust to move about. Consequently the dust tends to move from where the amplitude of the air vibrations is large to where it is small. That is, the dust collects into heaps at the nodes. Thus, the wavelength of the standing waves in air is determined from the separation of the dust heaps. Using the speed of sound in the air determined in Part I, the frequency of the vibrations can be obtained. The speed of sound in the rod is calculated using the length of the rod and the frequency of the vibrations. For this experiment the length of the rod is equal to 1/2 of a wavelength of sound (within the rod). We will use an aluminum rod, in which the speed of sound is approximately 5100 m/s at room temperature.
Let be the frequency of the vibration produced in the rod. This will also be the frequency of the corresponding vibrations in the air. Let be the speed of sound in the rod, [[lambda]]2 be the wavelength of sound within the rod, and correspond to wavelength of the vibration in the air. We then have
But, since , dividing(11.3) by (11.4) gives,
With the rod clamped at its center point, the length of the rod L is a half wavelength of the sound in the rod, or equivalently, . Thus,
where = 332 m/sec is the speed of sound in air at 0 deg.C and T is the temperature in degrees Celsius.