Standing Waves Lab To Determine Frequency Of Unknown Tuning Fork Mohammad Ihsan Wadid Partner(s): Daniel Rosen SPH3U1-1 Due date: October 12, 2023 Ms. Hrab Materials: - 1 1L graduated cylinder Water 1 clear acetate or PVC pipe 1 ruler 3 tuning forks of known frequency (128 Hz, 512 Hz, 4096 Hz) 1 tuning fork of unknown frequency Apparatus: Procedure: 1. 2. 3. 4. The graduated cylinder was filled up to approximately ¾ with water. Placed the graduated cylinder on the counter by the lab station. While still holding the clear acetate or PVC tube, it was submerged mostly into the water. The 128 Hz tuning fork was hit and held horizontally near the opening of the tube, ensuring not to touch the tube with the fork. 5. The height of the tube was adjusted until a higher intensity sound was heard, indicating a standing wave had been produced. 6. A ruler was to record the length between the water and the top of the PVC tube. 7. Steps 3-6 WERE REPEATED for each subsequent tuning fork (512 Hz, 4096 Hz, and unknown frequency). Observations: TABLE NUMBER. TITLE. CAPTION. Frequency (Hz) Smallest resonance length (m) (¼ λ) Wavelength (m) 512 0.075 0.30 128 0.10 0.40 4096 0.045 0.18 Unknown 0.14 0.56 This table provides information on the relationship between frequency, minimum resonance, and wavelength. The frequency is measured in hertz (Hz) and the smallest resonance in meters (m) per quarter length (¼ λ). It should be noted that the values in the table are multiplied by 4, because the size of the cylinder has changed from 1 liter to 4 liters. The resonance lengths for three specific frequencies: 512 Hz, 128 Hz, and 4096 Hz are 0.075 m, 0.10 m, and 0.045 m, respectively. Also listed is an "Unknown" frequency with a corrected minimum resonance of 0.14 m. The wavelengths corresponding to each frequency are also given in meters. This table contains important information for understanding the relationship between frequency, wavelength and resonance, and a correction factor should be considered when interpreting the data. Analysis: Wavelength vs Frequency graph The wavelength vs frequency graph created using the table values shows a clear relationship between these two variables. As the frequency increases, the wavelength decreases. We can see that the graph starts at 0.40 m at 128 Hz, touches 0.30 m at 512 Hz and then ends at 0.18 m at 4096 Hz. The graph provides important information about the relationship between the wavelength and the frequency, with the frequency as the independent variable. Wave speeds The equation used to calculate the wave speed is: v = λf 1. Tuning fork: 128 Hz v = 0.40m x 128Hz (x is used for multiplication) v = 51.2 m/s Here, we used 0.40m for the wavelength and 128 Hz for the frequency. We inputted the values into the equation and got 51.2 m/s as the wave speed for the tuning fork of 128 Hz. Now, we will repeat the same step with the other two tuning forks. 2. Tuning fork: 512 Hz v = 0.30 m x 512 Hz (x is used for multiplication) v = 153.6 m/s By repeating the same process as we did with the first tuning fork, we got 153.6 m/s as the wave speed for the tuning fork of 512 Hz. Now, for the last tuning fork. 3. Tuning fork: 4096 Hz v = 0.18 m x 4096 Hz (x is used for multiplication) v = 737.28 m/s For the last tuning fork, we received a wave speed of 737.28 m/s. Discussion Questions 1. Using the wavelength versus frequency graph, determine the frequency of the unknown tuning fork. Explain your process. - After using the wavelength vs frequency graph to determine the frequency of the unknown tuning fork, the frequency of the unknown tuning fork appears to be in negative values. This is due to the fact that the graph starts at 0.40 on the y-axis and 128 on the x-axis. After analyzing the graph, we observed that the graph will be landing somewhere in the negative quadrant of the graph due to the graph having a negative slope. 2. Based on the wavelength versus frequency graph, describe the mathematical relationship between frequency and wavelength. - Based on the wavelength versus frequency graph, the mathematical relationship between frequency and wavelength is an inverse relation. This is due to the graph starting at 0.40 on the y-axis and going down. 3. Frequency and wavelength are inversely proportional. This means that as the frequency increases, the wavelength will decrease as well. We observed 8192 Hz two times 4192, which is a data we already have in our table. Therefore, we could divide the wavelength of the frequency 4096 Hz by 2 in order to get the wavelength of 8192. For this, we will be using: f1 = λ/2 (let 8192 be f1) f1 = 0.56 m / 2 f1 = 0.28 m Therefore, the wavelength of a tuning fork with frequency 8192 Hz is 0.28 m. 4. How would the calculations in this activity change if this lab was investigating a standing wave in a string or in an open air column? Explain why. - If this lab was investigating a standing wave in a string or in an open air column, the calculations would change because the speed of the wave would be different. The speed of a wave depends on the properties of the medium through which it travels, such as its density. 5. Discuss 2 sources of error leading to inaccuracy or reduced precision with the results. Use the identify, quantify, rectify format. - The two sources that could lead to inaccuracy or reduced precision with the results are: ● Instrumental errors: This error can occur due to limitations or inaccuracies in the measuring instruments used in the experiment. For example, the instrument might not be accurate or sensitive enough to measure small changes while conducting the experiment. This error can be quantified by comparing the actual values with the values observed during the experiment. We can rectify these errors by ensuring that the measuring instrument is sensitive and accurate enough to measure values. ● Human error: This error can occur due to mistakes made by the people conducting the experiment. For example, the experimenter may incorrectly read the values during the experiment, which reduces the accuracy and precision of the values measured. We can quantify this error in the same way as the first error. That is, by comparing the measured values to the true values, or by having different experimenters on the experiment. This error can be rectified by making sure that the experimenters are properly trained and that they carry the knowledge to carry out the experiment properly, without the risk of errors. References Google Sheets: Sign-in. (n.d.). https://docs.google.com/spreadsheets/d/1bn0NnFXBqVWlgIn3AsTe21fHOoAtoc_TBsQ v6JGD9Fw/edit#gid=0 Masuzi, Masuzi, & Masuzi. (2018). Physics Reference Table Waves | Brokeasshome.com. Brokeasshome.com. https://brokeasshome.com/physics-reference-table-waves/
