Pre-Lab Questions: 1a. In the experiment, you will be using the speed of sound i

Question

Pre-Lab Questions:

1a.    In the experiment, you will be using the speed of sound in your metal bar to help determine the Young’s Modulus of that bar. So, you can’t use Young’s Modulus to find the speed of sound. What equation will you be using to find the speed of sound?

1b.    The equation you quoted above should have two terms (other than the speed of sound itself). For each of these terms, state what it is, and explain what you will do, in this experiment, to find it.

2.      If you were to take a 60.0 cm long steel bar, and heated it to the point that it would try to expand by 0.50 mm, what is the pressure you would need to apply, to keep it from expanding? (You may picture this as: it has already expanded by 0.50mm due to thermal expansion, and you then apply enough force to get it to contract back to its original length.) (Assume that all of the other properties of steel are independent of temperature.)

Explanation / Answer

1

Theoretically, the speed of sound in metal can be calculated from the equation vTheory =square root of ( Y / )

But we calculate the speed of the sound wave in the metal bar from equation Vm = fm * m

where Vm, m, and fm are the speed, wavelength and frequency of the sound waves in the metal.

The principles outlined above can be applied, also, to determine the speed of sound in a metal. Longitudinal standing waves are formed in the metal bar, by striking one end of the bar with a mallet.

With the bar clamped at its mid-point a node forms there while antinodes form at the free ends, as indicated in Figure 1. If the bar is vibrating in its fundamental mode, then the wavelength of the wave in the metal is equal to twice the length of the bar, =2L. If the frequency of the waves can be determined, the below equation can be used to calculate the speed of the sound wave in the metal.

The vibrating end of the bar produces sound waves in air with a frequency identical to that, at which the bar is vibrating, i.e., fm=fa.

where fa is the frequency of the sound waves in air. Thus, by measuring fa one can determine fm and, thus, calculate the speed of the sound wave in the metal bar from equation vm = m fm

where vm, m, and fm are the speed, wavelength and frequency of the sound waves in the metal. For the experiment, a sound sensor is used to collect the sound waves at the end of the metal bar. The computer uses a Fast Fourier Transform technique (FFT) to convert the sound waves to a spectrum of amplitude vs. frequency. With the rod or bar is clamped in the center and struck along its end it will produce a fundamental frequency and this frequency will be displayed along with some of it harmonics in the spectrum window, the largest peak amplitude is the fundamental frequency of the rod or bar. Using this frequency in conjunction with the wavelength (twice the length of the bar/rod) and from the equation the speed of sound in the bar or rod can be determine.

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