Inquiry: Speed of Sound in Metals
Purpose: To examine open tubes and calculate the speed in metals
Measurement of sound velocity in solids are usually done for thin rods but such measurements can also be made with thin pipes of any cross-sectional area. Rods are better because they can acquire more sound energy for the same size and result in a longer duration of the sound wave. The rods must have a suspension that makes possible the creation of a single frequency standing wave. For a given wave, if the position of the nodes and antinodes are known and its frequency is measured, then the sound velocity can be calculated by velocity = frequency x wavelength.
Most often, resonance in a rod is created by striking one of its ends. Initially such an impact creates many propagating waves with different frequencies. The frequencies that are not resonant dissipate quickly, leaving only a few standing waves of resonant frequencies. How many of them survive depends on the material, the suspension and the impact. The art of impact happens to be very important in the experiment. For rods suspended in the middle, a fundamental frequency standing wave usually survives longer than the other resonance waves and can be used for sound velocity measurements. Some impacts may not produce enough amplitude for the fundamental frequency. This is why impacts of different strength with objects of different masses, materials and shapes must be tried.
If you support the rod in the center by placing it in the clamp, and impact the end with a metal object, a clear mixture of a fundamental and a third harmonic appears on the oscilloscope screen. Later on, energy of the third harmonic dissipates and may even be partially transferred to the fundamental waves. In this phase, the computer measures a kind of "effective" frequency, which obviously must not be used for sound velocity calculations. Finally, only the fundamental persists.
We will use the Audio Spectrum Analyzer dB RTA app to measure frequencies in the metal rods.
- Find the velocity of sound in Aluminum (5100 m/s), Brass (3800 m/s) and Iron (5200 m/s) by measuring the frequency of the fundamentals and calculating percent errors. The lengths of the rods are Aluminum (90.0 cm), Brass (78.0 cm) and Iron (80.0 cm).
- Try to play the 2nd and 4th harmonics of the Aluminum rod. Make sketches of the waves in the rod and how the rods should be supported.
- When you play the fundamental frequency of the Aluminum rod what other harmonics are present?
- A 100 cm rod is vibrated at it's 5th harmonic. How many cm in from one end is the first node?