Velocity of Longitudinal Pressure in Sold Bars
Introduction
As opposed to the transverse waves, longitudinal waves are not easily visible. They usually take place in one direction. Whenever we want to generate a pulse in an oscilloscope, it is required that the wave travels in a single direction to avoid creation of seismic or spark points due to merging or collision of the waves. Both the longitudinal (compressional) and shear waves travel in the form of bulk matter although the later causes change in volume, shape or layer (Hanyga 15). In order to effectively discuss the elastic characteristics of an elastic material like bars, the young’s modulus must be calculated. This joins the effects of shears and longitudinal forces.
Introduction
The inertial nature of a medium and the ability to store potential energy are the primary determinants of a mechanical wave. Whenever a mechanical wave is experienced, its speed can be determined by the formula V=elastic propertyinertial property
Pressure waves are forms of mechanical waves with an audible range of frequency. Whenever the rate falls below that range (below 20Hz), they are referred as infrasonic waves. I the audible range fall between 20 Hz to 20,000 Hz, we refer to them as sound waves. Any other wave above the 20,000 Hz is called an ultrasonic wave. In solid materials, this pressure travels in the form of longitudinal or transverse waves. In the experiment, the materials will be subjected to longitudinal waves that will be allowed to propagate through the entire length (Ashby). These pulses are usually captured by an oscilloscope that generates square waves at a rate of about 10 μs. Such waves are then directed to a transducer that is in turn connected to one side of the bar. The transducer converts the pulses to pressure waves and passes it on to the bar where it travels all the way to the end of the length. The pulse is picked by the second transducer placed at the other end of the bar, converts the wave into electric pulses and passes it to the preamplifier. Both of the pulses, the direct and propagated are captured and displayed on different channels of the oscilloscope. There may be a time difference between the two as the propagated wave travels at a slower rate than the direct wave. Using the time difference, the velocity of the pressure wave can be calculated as V=L∆t..
Also, from the length, width and diameter values, the volume of the bar can be calculated asVolume =πR2 ×L. Given the mass is known, then the density of the material can be calculated fromdensity=mass/volume. The elastic properties are then determined from the Young’s modulus gotten from ∈=FL/∆LA; where F= force, L= length, ∆L= change in length and A is the cross-sectional area (Froman 265). Then, the velocity v=∈ρ.
∈=v2ρ
Precautions must be made to avoid disconnecting the transducers, preamplifier, and oscilloscope. The preamplifier has two types of signal connections and one for power that if mixed up will make the device blow up. All the connections must be checked before powering to avoid such eventualities.
The primary aim of the experiment is to calculate the elastic modulus of the given materials in order to determine the velocity of the longitudinal pressure. The distinction between the p-waves and shear waves is also assessed.
Apparatus
Greenstone, granite, diorite, norite, and copper
Cradle
Oscilloscope
Vacuum grease
Piezoelectric transducer
Power supply
Printer
Balance
Caliper
Preamplifier
Cables
Ruler
Procedure
The pulse generator, amplifier, and oscilloscope were all checked to ensure that the settings and connections were correct and that they all were operational.
The wires and cable connections the piezoelectric transducer were checked. Schematics were followed to ensure that the connections were ok.
After ascertaining that all the apparatus were operational and well set, the length and diameter of greenstone, granite, diorite, norite, and copper were measured using a ruler and caliper respectively
The value was recorded in the appropriate tables
The weights of the bars were also measured using the balance and the values recorded accordingly.
The oscilloscope was then set in a single trigger mode
A thin layer of vacuum grease was applied on the transducer’s membrane
The transducer was then brought on head in contact
A pulse was then sent from the pulse generator
When the two pulses were displayed on the oscilloscope screen, then the oscilloscope was set to take the readings
The transducer was then coupled to the ends of each bar to be measured in turns. The cradle was used to hold the transducer in tight contact with the end of the bars.
A pulse was then sent from the generators, and that was displayed on the screen. Channel one represented the direct pulse while channel 2 represented the propagated pulse.
The time intervals and settings were adjusted to maximize the precision so that the time difference between the two arrivals (∆t) could be easily determined.
The pulses were captured and saved for analysis
Figure 1: Schematic of the experiment
Results and Analysis
The dimensions of the materials were as follows
The waves captured by the oscilloscope were
Image 1: Greenstone Image 2: Granite
Image 3: Norite Image 4: Copper
Image 5: Steel Image 6: Diorite
Image 7: Glass
On calculating the density and volume via Excel spreadsheet, the Young’s modulus of elasticity for each material was gotten as shown in the table below
Conclusion
After calculation, we find that the materials have different Young’s modulus of elasticity. Steel has the largest (1.79033E+11 N/M2) while Norite has the smallest. From the velocity of the longitudinal pressure was easily calculated from the value of length and change in time. Although there could have been errors in the setting and taking readings, the results show the differences that are efficient. The higher the Young’s, the greater the amount of stress the material can withstand(Saperstein and Fainman 47).
References
Ashby, M. F. Materials Selection In Mechanical Design. Oxford, OX: Butterworth-Heinemann, 1999. Print.
Froman, Darol K. "Young's Modulus Determined With Small Stresses". Phys. Rev. 35.3 (1930): 264-268. Web.
Saperstein, Robert E., and Yeshaiahu Fainman. "Information Processing With Longitudinal Spectral Decomposition Of Pulses." Appl. Opt. 47.4 (2007): A21. Web.
Hanyga, Andrzej. Shear Waves. Warszawa: Państwowe Wydawn. Naukowe, 1975. Print.
