The Speed of Sound in a String - Lab Report Example

Running head: To find the speed of sound in a string Student’s name Institution Course Professor Date of Experiment Date of Submission Abstract This laboratory report discussed the standing waves in order to determine the speed of sound in a string. The objectives of the experiment were to be familiar with the equipment such as a vibrating device, a string, a set of weights, and a tension measuring device, a tape measure and a top loading balance and also to find out the relationship that existed between the tension of the string, the velocity and wavelength and the number of standing waves formed. The vibrating device was adjusted in order to produce several standing waves that had varied wavelengths. During this experiment in order to achieve its objective various measurements were done. These included the frequency of the vibrator, weight used and the wavelengths. The oscillator was adjusted to a frequency of 15Hz and the string was tension with a 200g weight. Graphs of frequency and inverse of wavelength were plotted and a slope was calculated to produce the value of the speed of sound for each tension. Table of Contents Abstract 2 Table of Contents 3 1.0Introduction 4 1.1Theory 4 2.0Methodology 6 2.1Procedures 6 3.0Results and calculations 7 4.0Discussion 12 5.0Conclusions 13 6.0 References 14 1.0Introduction This laboratory report discussed the standing waves in order to determine the speed of sound in a string. And also to find out the relationship that existed between the tension of the string, the velocity and wavelength and the number of standing waves formed. The oscillator was set to a frequency of 15Hz and the string was tension with a 200g weight. The frequency was adjusted till a standing wave was produced (Giordano, 2012). The main objectives of this experiment were to Develop the research skills Familiarize with the below mentioned equipment; a vibrating device, a string, a set of weights, and a tension measuring device, a tape measure and a top loading balance Understand the standing waves Establish the relationship that exists between the velocity of a wave in vibrating string and mass per unit length, frequency and tension. Investigate the speed of sound in a string 1.1Theory A standing wave can be referred also as a stationary wave. This wave is able to remain in a constant motion because the medium is moving in the opposite direction to the wave (Giordano, 2012). This wave is created by the sum of two counter-propagating waves having equal frequency and amplitude. The speed of a wave travelling along a stretched string (V) is directly proportional to the square root of the tension (T) over the linear density (µ) (Giordano, 2012). V= The speed of sound in the string in m/s1 T=The tension in the string in N µ= The mass per unit length (linear density) of the string in kg/m1 Wavelength, λ of the string of the standing wave can be determined from the formula λ = 2L/n Where L = Length of the stretch string n= Number of segments in the string The velocity of the wave in a string can be expressed as V=f λ Where V= The speed of sound in ms1 f= The frequency in Hz λ= The wavelength in m Thus the speed of a wave is dependent on the frequency, wavelength and the period. Additionally, the velocity of a transverse wave on a string is also dependent on tension in the string and mass per unit length (linear mass density) (Lerner, 1996). 2.0Methodology Among the equipment used during this experiment included; A vibrating device A string A tape measure A top loading balance A set of weights A tension measuring device 2.1Procedures After being acquainted with equipment to be used during this experiment, the oscillator was set to a frequency of 15Hz while the string was tensioned with a weight of 200g. The frequency of a vibration on the string was adjusted until a standing wave was displayed. The end of the vibrating blade was looked at to ensure that a node was present at the point where the string attaches. The blade rattling against the case indicated a bad node. The frequency of the string was altered so that it could give five different standing waves and recorded the weight used, the tension in the string, and the frequency of the oscillator and the wavelength of the standing wave. This procedure was repeated with other five different weights. The length and the mass of the string was measured and recorded and used to give a value for its mass per unit length in kg/m1. For each tension, a graph of frequency against inverse of wavelength was plotted in order to obtain the speed of sound in m/s1. 3.0Results and calculations The results were tabulated as illustrated below The length of the string= 2.4m The weight of the string = 13g The linear mass density = 4.44 * 10-3 kg/m Mass (g) Frequency (Hz) Tension (N) Wavelength, λ (m) 1/λ 200 15 2.2 2.4 *(2/3) = 1.6 0.625 20 2.2 2.4 *(2/4) =1.2 0.83 25 2.2 2.4 *(2/5) =0.96 1.042 30 2.2 2.4 *(2/6) =0.8 1.25 35 2.2 2.4 *(2/7) =0.69 1.45 Mass (g) Frequency (Hz) Tension (N) Wavelength, λ (m) 1/λ 100 15 1.3 2.4 *(2/4) = 1.2 0.83 19 1.3 2.4 *(2/5) = 0.96 1.042 23 1.3 2.4 *(2/6) =0.8 1.25 27 1.3 2.4 *(2/7) = 0.69 1.45 31 1.3 2.4 *(2/8) = 0.6 1.667 Mass (g) Frequency (Hz) Tension (N) Wavelength, λ (m) 1/λ 150 13.1 1.8 2.4 *(2/3) = 1.6 0.625 15.1 1.8 2.4 *(2/7) = 0.69 1.45 17.2 1.8 2.4 *(2/4) = 1.2 0.83 22 1.8 2.4 *(2/5) = 0.96 1.042 26.2 1.8 2.4(2/6) = 0.8 1.25 Mass (g) Frequency (Hz) Tension (N) Wavelength, λ (m) 1/λ 250 17 2.8 2.4(2/3) =1.6 0.625 22.3 2.8 2.4(2/4) =1.2 0.83 28 2.8 2.4(2/5) =0.96 1.042 39 2.8 2.4(2/6) =0.8 1.25 39.6 2.8 2.4(2/7) =0.69 1.45 In part one, four graphs of frequency of the string against the inverse of the wavelength are shown below The gradient or = (27.85-9.32)/ (1.139-0.370) 18.53/0.769 24.10m/s = (34.41-8.70)/ (1.816-0.481) 25.71/1.435 17.92m/s = (29.42-7.36)/ (1.380-0.343) 22.06/1.037 21.73m/s = (44.80-11.38)/ (1.546-0.424) 33.42/1.122 29.79m/s 4.0Discussion In part two of the experiment, the formula below was employed to find the speed of sound in a string. V= The speed of sound in the string in m/s1 T=The tension in the string in N µ= The mass per unit length (linear density) of the string in kg/m1 The following values were recorded The length of the string= 2.4m The weight of the string = 13g The linear mass density = 4.44 * 10-3 kg/m The calculations can be simplified in a table Tension (N) Linear mass density (kg/m) Speed of the sound in a string (M/s) 2.2 4.44 * 10-3 kg/m 22.26 1.3 17.11 1.8 20.13 2.8 25.11 The values of speed of sound in a string in part one and two can be compared as follows and the percentage error is calculated Mass in the string Value of C in part 1 Value of C in part 2 Percentage error (%) 200g 24.10 22.26 7.72% 100g 17.92 17.11 4.52% 150g 21.73 20.13 3.6% 250g 29.79 25.11 15.71% From the above table, the percentage error for the values of the speed of sound in the string is minimal. The speed of a travelling wave in a stretched string can be calculated by the mass per unit length of the string and the tension of the string and also by the frequency and the wavelength. 5.0Conclusions In this laboratory experiment, the standing waves were able to be understood and the speed of sound in a string investigated. There is relationship between the tension in the string and the wavelength in the standing wave and the relationship between the frequency of oscillation of the string and the number of oscillations. Among the source of errors were; the parallax, the weighing error and the frequency of vibration being not constant. 6.0 References Giordano, N. “College Physics”, New York: Cengage Learning. 2012. Print. Lawrence S. Lerner, “Physics: for scientists and engineers; Modern Physics: for scientists and engineers”, ones & Bartlett Learning, 1996.print Read More