Lab 2 - This is a Lab report for a physics experiment on Standing Waves PDF

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This is a Lab report for a physics experiment on Standing Waves ...

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Lab Report for Experiment 14 Standing Waves

Shivam Agarwal Lab Partner: Anton Draayer TA: Kunpeng Mu May 18, 2016

Introduction: The experiment had two investigations and the main goals of the experiment were to study standing waves of a string, to examine the relationship between string tension and wave velocity, to study standing waves in an air column and to measure the sound velocity. Both the investigations were very different to each other and to conduct the experiment, we had a 120Hz vibrator, 2 stands with 2 rods, 3 rod clamps, 1 pulley, a short rod with a string clamp, a meter stick, a sound wave apparatus, 3 tuning forks with different frequencies and brass weights. In the first investigation, we created standing waves on a string and also measured the mass of the weights we were adding to the bucket to get the different number of nodes on the string. We also measured the distance between the nodes which helped us calculate various values of the string including the wavelength, tension, density and the speed of the wave. These values helped us make a graphical analysis of the standing waves using the tension of the string and the square of velocity. In the second investigation, we used three different tuning forks with different frequencies to create standing longitudinal waves in an air column. As we struck the fork over the column, we measured the position where the sound from the column was the loudest. Using the position and the frequency of the fork, we calculated the wavelength, speed and the period. Using all these values we did a graphical analysis of these values by plotting a graph using the wavelength and the period of the waves. All the calculations and the graphs were drawn using Microsoft Excel and all these values are shown under the data analysis parts of the two investigations.

Investigation 1: Setup and procedure: In this investigation, we had to create standing waves on a string. So we first set two rods about a meter apart from each other and then attached the two rods by a string. On one end of a string, we attached a bucket and the other end of the string was on the other rod on which we clamped the electromagnetic vibrator and the string holder. The other rod had a pulley through which the string passed and the bucket was hanging. As the investigation was set up, we then switched the vibrator on due to which the string started to vibrate and we were able to see different number of nodes on the string. To get different number of nodes, we started adding brass weights to the bucket and so we recorded the distance between nodes for 3, 4, 5, 6, 7 and 8 number of nodes. Using these values, we also calculated the average distance, the wavelength, the velocity and the tension in the string. After calculating these values, we made a graph using the velocity squared and the tension force of the string to find out the mass per unit length of the string. Data and analysis:

v^2 vs f 25000

20000

f(x) = 3440.03 x + 1813.2 R² = 1

V^2

15000

10000

5000

0

0

1

2

3

4

Tension force v^2 vs f

Linear (v^2 vs f)

Linear (v^2 vs f)

5

6

We calculated the average distance between the nodes by adding the distance between all nodes and then dividing it by the number of nodes. The wavelength of the nodes was then found by multiplying this distance with 2. The error in the wavelength as calculated by the ruler was ± 0.0005 m. As we had the wavelengths, we calculated the speed of the wave using v = λf The frequency of this investigation was 120 Hz and we had the different values for the wavelength, due to which we were able to calculate speed and the error in the sped was calculated using the formula: σv = (v*σT)/ (2T) We also found the tension in the string by multiplying the mass and the acceleration due to gravity. The error in this force was equal to that of the wavelength as it was shown by the ruler which was ±0.0005m. Then using the graph above, we found the mass per unit length by using the equation: v = (T/μ) 0.5

The string density we found came out to be 0.28689 but the actual density of the string was 0.32

Investigation 2: Setup and procedure: In this investigation, we had to create standing longitudinal waves. To setup this investigation, we had a plastic tube connected to a reservoir that was attached to a rod. This tube was filled with water. We had the tuning forks, which we struck on top of the tube and the other partner moved the reservoir up and down to manage the water level in the tube. As we struck the tuning fork, we started to hear sounds over the tube. We then started to observe and note the position on which the sound heard was the loudest. We repeated the process three times with tuning forks of different frequencies. We also multiplied the position value with 3 and marked the other position which was about three times the old position on which the sound would be the loudest. We then

measured these values which helped us find the period, wavelength of the wave and the speed of the sound. We also made a graph using the period and the wavelength. Data and analysis:

Wavelength

Wavelength vs Period 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0

f(x) = 341.62 x R² = 1

0

0

0

0

0

0

0

0

0

Period Wavelength vs Period

Linear (Wavelength vs Period)

Average speed of sound: 341.62 This was calculated by adding all the speeds of sound and then dividing by three.

Conclusion: Investigation 1 – Calculated String Density: 0.28689 Theoretical String Density: 0.32 The error in the calculated and the theoretical value can be caused due to the parallax error as it is very difficult to count the number of nodes as the number increases. It is also very difficult to see where the node starts and ends which causes the distance between the nodes to be uncertain. The uncertainties in all the other errors also cause the values to be a little different. Investigation 2 –

Calculated speed of sound: 341.62 m/s Theoretical value: 343 m/s The calculated value is very close to the theoretical value and the error that could have caused in this to happen would be the way the measurement was handled as it was not easy to accurately measure the position where the loudest sound was produced.

Questions: 1) Speed = wavelength * frequency = (0.65 m * 2) * 248 Hz = 322 m/s 2) Tension = (v^2 * µ) = (322^2 * 0.0005) = 52 N 3) 0.5* λ = 0.48 m  λ = 0.96 m F = v/ λ  343/0.96 = 357 Hz 4) Resonance occurs at 0.25 λ = (1000/512)  λ = 0.4883 AND Resonance occurs at ¾ λ = (1000/512)  λ = 1.46 Hence the separation between maxima = 1.46 – 0.4883 = 0.97m

Acknowledgement: I would like to thank my T.A. – Mr. Kunpeng Mu and my lab partner Anton Draayer who helped me in the lab.

References: O.Batishchev and A. Hyde, Introductory Physics Laboratory, Hayden-McNeil, 2016...