Phys_1080 - 11 Speed of Sound. Buseong Jang. Group G

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Feb 20, 2024

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Lead Author: Buseong Jang Date: 11.17.2020 Computer Operator: Jackson Smith Lab Day: Tuesday Principle Investigator 1: Buseong Jang Lab Time: 3pm~4:50pm Principle Investigator 2: Standing Waves and Sound - Lab Learning Outcomes Students should be able to: • define the speed of a wave. • identify the sound as a wave. • explain when resonances occur in a closed-ended tube. • figure out the relationship between the length of the tube and the wave’s wavelength. • by using the definition of the speed of a wave, to calculate its numerical value. • critically think of which of the obtained variables in this activity they should use to determine the speed of sound. • evaluate their results. Apparatus • Plastic tube • Clamp • Glass cylinder filled with water • Tuning fork (1024 Hz), tuning fork striker • Half meter stick • Velocity of sound apparatus • Microphone • Thermometer mounted in front of lab Loud Lab Warning Date Modified: June 26, 2019 Speed of Sound Page 1 of 9

This lab will have a lot of sound. Note: Students often make measurements mistakes because they hear something from the next table. Always verify your measurements before you record them. Part 1: Hands on Sound Introduction The goal of this lab is to measure experimentally the speed of sound. We will need to set up and use a sophisticated apparatus that will help us determine the speed of sound. But since we are measuring speed, why not to use the general definition of speed which is measuring the distance that an object travels and divide it by the required time that it needs to cover that distance? Could your group perform this activity in the classroom to obtain the value of the speed of sound by using a meter-stick and a stopwatch? Discuss within your group and explain your reasoning. No, because we need some sort of device to measure the sound waves since they are invisible. Setting up the Apparatus 1. On your table, you should have a graduated cylinder. If it is not filled with water, fill it with water until only a few centimeters remain at the top of the cylinder. 2. Place the tube into the water so that it is almost entirely submerged, with about 2 cm of distance between the tube and water level in the graduated cylinder. Note: In this portion of the lab all the distances measured will be from the top of the tube to the water level. You should use a separate ruler or meter stick to doing this. Observing-Investigating the Phenomenon 1. Strike the 1024 Hz tuning fork on the striker. Hold it about as far away from you as the water cylinder is. Then, move it over the tube in the cylinder. 2. Now move the inner tube slowly upward and listen to the tube. What do you notice about the volume of the sound coming from the tube and tuning fork? You should move over at least 10 cm of distance. What do you notice in the sound level as you slowly keep moving the inner tube upward? The sound is increasing when it gets close to a resonance frequency and then fades away when continuing to move up, eventually coming to another resonance frequency and becoming louder again. Taking Measurements Date Modified: June 26, 2019 Speed of Sound Page 2 of 9

1. Now, repeat the same procedure as before recording the distances (measured from the top of the tube until the water level) where you observe all the anomalies in the tone. These anomalies are called resonances. Record your measurements on the following table. Resonances Length (cm) 1st 50 2nd 64 3rd 75 1. Take the differences between the second measured length and the first, and the difference between the third and the second measured length. Do you notice any patterns in the measured lengths where you observe these resonances? If you don’t, see if you missed any points; failing that you might want to ask your TA for some help. The difference between the first and the second measurement is 14cm and the distance between the third and the second measurement is 11cm. The only noticeable pattern is that the distance got smaller by 3cm between these new measurements. This relates to wavelength. 2. This pattern of distance must be related to the sound. What property of sound could this be related to? Remember that sound is a wave and that waves are defined by a frequency and a wavelength. The wavelength of the soundwave is related to this. Resonance occurs when it begins with node and finishes with antinode. 3. The open side of the tube is where the air is free to move, therefore there is the antinode (A). The bottom of the tube is where the air cannot move (water level), a location of no displacement, therefore there is a node (N). In other words, when resonances occur, the end of the closed end of the tube has a node and the open end, an antinode. The first antinode of the wave produced is the first resonance we observe. Date Modified: June 26, 2019 Speed of Sound Page 3 of 9

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4. The following figure illustrates the first harmonic that produces resonance. In the space provided below, draw the two next harmonics for the resonances you observe along with the relation between the wavelength and the length of the tube, as shown for the first antinode. Note: the referred “tube” is the tube between the top of the inner tube (open end) until the water level (closed end), the length of which you just measured in question 1. Draw the wave until the third antinode is met and write the mathematical relationship between L 3 and λ Draw the wave until the second antinode is met and write the mathematical relationship between L 2 and λ The first antinode is met at a quarter of a wavelength (distance between one node and the next antinode is λ/4) 𝐿 = λ /4 Date Modified: June 26, 2019 Speed of Sound Page 4 of 9 L 3 = 7 5 c m L 2 = 6 4 c m L 1 = 5 0 c m

Analyzing the Results 5. Since you already have calculated the values for the differences between L 2 -L 1 and L 3 -L 1 , now, do the same thing using the relationships for those lengths as determined on the previous question. L 2 − L 1 = 3 λ 4 − λ 4 = ¿ λ /2 L 3 − L 4 = 5 λ 4 − 3 λ 4 = ¿ λ /2 6. How do the obtained results compare to the values for those differences? Can you now calculate the wavelength? Show your work. The results match up with the values correctly. yes you can calculate the wavelength. wavelength(λ)= 0.28m 7. Great! Now, you ‘ve got all the needed information to calculate the speed of sound! Refer to the introduction question and compare the method of using stopwatches and meter-sticks with the activity that you developed in this lab to figure out what is the value of the speed of sound. Discuss and compare the two methods. The method of calculating the speed of sound through measurements of resonance frequencies is much more accurate vs the idea of using measuring sticks and a stopwatch. The speed of sound is very fast and invisible so the idea of just using our ears to hear the differences and measure with a stopwatch would be completely unscientific. The use of precise measurements and calculations leads to a more precise answer. 8. Now, calculate the speed of sound using the variables that you have obtained in this activity. Date Modified: June 26, 2019 Speed of Sound Page 5 of 9

Frequency=1024 Hz λ=0.28 m Speed=1024Hz*0.28 m= 286.72m/s Concluding About the Results 1. Is your result reasonable, how you know? (Check your units.) Yes, because they are all very similar speeds.(units : m/s) Part 2: Using A Sophisticated Apparatus We are now going to move to a more refined apparatus to continue with this experiment using more frequencies. You should have noticed a pattern in the resonance. We will look for that pattern now amongst several different frequencies. Learning Unit 1: Setting up the Apparatus 1. The microphone should be plugged into Analog Input A on your interface by using a PASCO BNC adapter. You should also have the two banana cables connecting ‘ Output 1’ and the speed of sound apparatus. a. Start Capstone and set Analog input A to Voltage Sensor. Then open the “Signal Generator” window. The “Signal Generator” window icon is in the same column as the “Hardware Setup” icon. Note: There is a pin icon in the upper right of the “Signal Generator” window; this pin will make your page not overlap this window. You will need to keep this window open for most of the rest of this lab. b. The signal generator will allow the speaker in the apparatus to act as an adjustable tuning fork. In the signal generator, you can adjust the following: i. Waveform: Keep this set to “Sine” and do not adjust it. ii. Sweep Type: This should be set to “Off” and not adjusted. iii. Frequency: This is where you set the frequency you are using. The tuning fork has a frequency of 512 Hz. That is not a bad place to start this lab. iv. Amplitude: This is the strength of the sound created in the lab. For this lab, 0.8 Volts work well. v. Voltage offset & Limits: Both should be left at 0 and 15, respectively. Date Modified: June 26, 2019 Speed of Sound Page 6 of 9

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c. Place the scope, that is the second icon on the right. The Scope has an advantage that it shows the sound wave when you are taking data. There are two helpful settings that you can use, Fast Monitor Mode and Activate and Control Scope Trigger. • Fast Monitor Mode: Allows real-time monitoring of a graph without using too much memory on the computer. You should select this when using the scope. It is next to the “Record” button. This causes the “Record” button to become a “Monitor” button. • Activate and Control Scope Trigger: It is the red arrow pointing up in the display bar. This allows the scope to appear more stable. By clicking this button the shape of the sound will start on an upslope and should remain in one place. Observing-Investigating the Phenomenon 1.Set up the speaker for a known frequency, e.g. starting with 512 Hz. 2. Slowly pull the piston handle out increasing the air column length. 3. Do you notice an increase in the sound level as on the previous activity? d Note: It might be very difficult to differentiate the sound coming from your group from all the sounds coming from the other tables. Therefore, it’s more efficient to observe the increase in voltage amplitude in the scope that you just have set up. 4. Describe what do you observe as you slowly pull the piston handle out increasing the air column length. An increase in amplitude of the wave as it nears a resonance frequency and then a decrease in the amplitude as it moves away from a resonance frequency. Taking Measurements 1. Each time that you observe the voltage amplitude to be maximum, just before it starts shrinking again, you should record the distance of tube’s length. Therefore, you should first construct a table. Take measurements of tube’s length for the first two resonances for each set of the frequencies. Remember that n=1 indicate the first resonance you meet, and n=3 the second one. Frequency (Hz) n L 512 (1 st resonance) 1 40cm 512 (2 nd resonance) 3 42cm Date Modified: June 26, 2019 Speed of Sound Page 7 of 9

1024 (1 st resonance) 1 9cm 1024 (2 nd resonance) 3 22cm 2048 (1 st resonance) 1 1cm 2048 (2 nd resonance) 3 9.5cm Analyzing the Results 1. The goal of today’s activities is to calculate the speed of sound. Since the sound is a wave, its value depends on the wavelength and the frequency. You already have your frequencies on the table, however not the wavelength. Do you have enough information on your table already that will help you find the wavelengths for each frequency? If so, how are you going to calculate the wavelengths? Date Modified: June 26, 2019 Speed of Sound Page 8 of 9

Yes,n3-n1=λ/2 λ =2(n3-n1) 2. Now, by using the same method you used on the first activity, obtain the wavelength for each set of frequencies, and calculate the speed of sound. Do not forget to include units on the column headings . Frequency (Hz) L 2 -L 1 (cm) λ s sound 512 2cm 0.04m 20.48m/s 1024 13cm 0.26m 266.24m/s 2048 8.5cm 0.17m 348.16m/s Summary 1. The speed of sound in air has been found to depend on the temperature of the air. That relationship is s sound = (331.46 + .605 T) m/sec. The T is the temperature of the room in degrees Celsius. Calculate the speed of sound at the room temperature using the above equation. 331.46 + .605 (25) = 346.585 m/sec at 25 degrees celsius. 2. Now, based on your outcome can you think of why do you see first the lightning before you hear the thunder? Because light moves faster, around 3x10^8 m/s, compared to the speed of sound, 346.585 m/s. Date Modified: June 26, 2019 Speed of Sound Page 9

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