Introduction

      The measurements of sound velocity in metals are usually done for thin rods. They can also be performed for thin pipes of any constant cross-sectional shape. Rods are better, of course, because they can acquire more sound energy for the same size and result in long duration of the sound wave.
      Such rods or pipes must have a support which makes possible the creation of a single frequency standing wave. If a single support is applied right in the middle, a longest lasting will be standing wave with a fundamental frequency (first harmonic) . This wave has a node in the middle and two antinodes on the both ends of the rod or pipe. Oscillations of both ends of the rod can be easily detected with the tip of your finger. When two supports are arranged at one quarter and three quarters of the rod (pipe) length, good conditions for a lasting second harmonic is created. This standing wave has two nodes over the two supports and three antinodes. Two of them on the both ends and third in the middle. Therefore a wavelength     for the first harmonic is equal to the double length of the rod (pipe), and for the second harmonic is equal to the length of the rod (pipe). Similarly we can create good conditions for a third harmonic placing two supports at one sixth and five sixth of the rod length.
      If somehow we would be able to measure the frequencies  f  of these harmonics, then the speed of sound  c can be calculated from the formula

c  =     f .

Moreover, we also would be able to calculate Young modulus  Y  for the rod (pipe) material using the theoretical formula which relates the speed of sound to the Young modulus and the density  of the material

c  =  [ Y /  ] ^½   .

This relation resembles very much the relation for velocity of transverse waves in a string. If the Young modulus is replaced by tension in the string and the ordinary density by a linear density of the string, then the mentioned relation for transverse waves in the string is recovered.
      The fact that speed of sound in metals and other solids must be dependent on their Young module can be easily justified. As a standing sound wave resides in a thin solid rod this rod undergoes a tiny mechanical vibrations that can be tested with the tip of your finger. In other words the rod elongates and shrinks periodically under a pressure exerted by the wave. But Young modulus relates pressures to elongations of the rod.

     Experimental

      A simple setup for standing waves frequency measurements is shown in Fig. 1. Striking the rod at the impact end we deliver there some mechanical energy with a wide range of frequencies. Some of these frequencies are resonance frequencies for the rod and they persist there longer in the form of  standing waves. The related vibrations of the rod ends are creating sound waves of the same frequency in the surrounding air. These waves are picked up by the microphone where an oscillating voltage of the same frequency is produced.  After amplification this voltage is sent to the oscilloscope or frequency meter. A moment after the rod is struck a sinusoidal signal related to the most persistent standing wave will be established on the oscilloscope screen (see Fig. 2). Counting number of half periods of this signal across the oscilloscope screen and a total time they occupy there, we can estimate the signal period T  (see Fig. 2). Its inverse is the frequency of the signal. The measurements of frequency with help of oscilloscope are interesting because they are showing time evolution of different standing waves established right after the rod impact (for more details see the article by M.T.Frank and E.Kluk , Phys.Teach. 29, 246 (1991)), but their accuracy is not very impressive.

Fig. 1.   Experimental setup		Fig. 2.  Frequency measurements

     How to make a simple amplifier for a Radio Shack microphone

      The microphone amplifier schematic is presented in Fig. 3. It shows how electronic components can be arranged on a half of a predrilled board. Specifications of the components are shown in the table below. The amplification of the input signal ranges from 100 to 1000 and depends on adjustment of the 100 K potentiometer. After the board is mounted with help of the machine screws and spacers on the bottom of the aluminum box, an additional hole securing access to the 100 K potentiometer must be drilled in the top of the box. The battery holder, switch and input, output jacks should be mounted on the sides of the bottom part of the box.

Fig. 3.   Schematic of microphone amplifier

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