Lab Speed of Sound Abstract: The apparatus consisted of a plastic tube filled with water linked to a water container. This container could be displaced vertically to change the water level. We would then make a tuning fork vibrate above the pipe and change the water level until the resonance was at maximum intensity. The velocity of sound is 330 ms-1, the relationship between velocity, frequency and wavelength is represented by the formula v= ƒ λ Apparatus: • • • Resonance tubes (with length scale marked on the tube). Tuning forks (range 500 to 1040Hz) and rubber hammer. Thermometer (one for the class) Theory: A sound wave is a pressure disturbance that travels through a medium by means of particle-toparticle interaction. As one particle becomes disturbed, it exerts a force on the next adjacent particle, thus disturbing that particle from rest and transporting the energy through the medium. Like any wave, the speed of a sound wave refers to how fast the disturbance is passed from particle to particle. While frequency refers to the number of vibrations that an individual particle makes per unit of time, speed refers to the distance that the disturbance travels per unit of time. Always be cautious to distinguish between the two often-confused quantities of speed (how fast...) and frequency (how often...). Since the speed of a wave is defined as the distance that a point on a wave (such as a compression or a rarefaction) travels per unit of time, it is often expressed in units of meters/second (abbreviated m/s). In equation form, this is speed = distance/time The faster a sound wave travels, the more distance it will cover in the same period. If a sound wave were observed to travel 700 meters in 2 seconds, then the speed of the wave would be 350 m/s. A slower wave would cover less distance - perhaps 660 meters - in the same time of 2 seconds and thus have a speed of 330 m/s. Faster waves cover more distance in the same period. Experimental procedure: 1. Measure the room temperature of the air and record it in Data Table 1. 2. Adjust the water level until the can is essentially empty when the tube is almost full. The water level in the tube should come to at least within 0.050m of the open end of the tube. It may be necessary to remove some water from the can when the water level is near the bottom of the tube. 3. Clamp a tuning fork above the top of the tube, and one partner should strike it repeatedly with the rubber hammer. Keep the fork vibrating continuously with a large amplitude. With the tuning fork vibrating, another partner should slowly lower the water level from the top while listening for a resonance. The sound will be very loud when a resonance is achieved. Try to measure the position of each resonance to the nearest millimeter. Raise and lower the water level several times to produce three trials for the measured position of the first resonance and record the values in Data Table 2. Record the frequency of the tuning fork in Data Table 2. 4. Repeat the procedure in Step 3 to locate as many other resonances as possible. Depending upon the frequency of the tuning fork, either three or four resonances should be attainable. Record in Data Table 2 the location of resonances that are attained. 5. Use a second tuning fork of different frequency and repeat Steps 1 through 4. Record in Data Table 3 the frequency of the tuning fork and the position of as many resonances as are attained. Data Table and calculations: Data table 1 Room temperature = 20.5*C Speed of Sound=343.94 Data Table 2: Frequency Fork one =512 Hz L1(m) L2(m) L3(m) L4(m) 0.03 0.115 0.108 0.29 0.02 0.47 0.109 0.30 0.025 0.118 0.203 0.32 Data table 3: Frequency Fork two =1024 Hz L1(m) L2(m) L3(m) L4(m) 0.043 0.14 0.275 0.32 0.042 0.135 0.273 0.33 0.043 0.145 0.278 0.325 Calculation table 1: ̅̅̅ 𝐿1 =0.025 αL1=0.0028 λ1=0.132 λ̅ =0.1805 ̅̅̅ 𝐿2 =0.116 αL2=0.000419 λ2=0.174 αλ= 0.003 ̅̅̅ 𝐿3 =0.199 αL3=0.692 ̅̅̅ 𝐿2 =0.14 αL2=0.0023 λ2=0.229 0.16αλ= ̅̅̅ 𝐿3 =0.273 αL3=0.00144 V=f λ =92.41 ̅̅̅ 𝐿4 =0.303 αL4=0.01766 λ3=0.1255 % Error= 73% Calculation table 2: ̅̅̅ 𝐿1 =0.046 αL1=0.00099 λ1=0.138 λ̅ =0.201 ̅̅̅ 𝐿4 = 0.325 αL4= λ3=0.136 V=f λ =295.82 % Error= 40% Conclusion: This lab taught me a lot about resonance. I learned that speed of sound is changed according to the temperature in the room at the time. I also learned how to find the antinodes of a standing wave. This was a challenging lab considering we were finding definite values in the lab and it was based on the way we did the lab if we had the right numbers. Answer question: Question 1 What is the equation that relates the speed V, the frequency f, and the wavelength l of a wave? Answer: The relation between the speed v, the frequency f and the wave length λ of a wave is given by v=ƒλ Question 2: How are standing waves produced? Answer: Standing waves are produced due to the superposition on of two progressive waves of same wavelength travelling in opposite directions between two fixed ends. Question 3 What name is given to a point in space where the wave amplitude is zero at all times? Answer: The point where the amplitude of the wave is zero all the time is called the node point Question 4 What name is given to a point in space where the wave amplitude is a maximum at all times? Answer: The point where the amplitude of the wave is maximum is called the anti node. Question 5 What are the conditions that must be satisfied to produce a standing wave in a tube open at one end and closed at the other end? Answer: If one end is closed, a node must exist at that end because the movement of air is restricted. If the end is open, the elements of air have complete freedom of motion, so an antinode exists. Question 6 For an ideal resonance tube an antinode occurs at the open end of the tube. What property of real resonance tubes slightly alters the position of this antinode? Answer: Increasing the diameter of the tube will increase the distance Question 7 Student using a tuning fork of frequency 512Hz observes that the speed of sound is 340m/s. What is the wavelength of this sound wave? Show your work. Answer: speed and wave length related by v=fλ λ = v/f = 340 m/s/ 512 Hz = 0.66406 m Question 8 A student using a resonance tube determines that three resonances occur at distances of L1=0.172m, L2=0.529m, and L3=0.884m below the open end of the tube. The frequency of the tuning fork used is 480Hz. What is the average speed of sound from these data? Show your work. Answer: For a open pipe, the wave lengths for the given lengths are λ1= 4L1 = 4(0.172 m) = 0.688 m Hence the velocity v =f λ1 =480 Hz (0.688 m) = 330.24 m/s λ2 = 4/3 L2 = 4/3 (0.529 m) = 0.705 m Hence the velocity v = fλ2 = 480 Hz (0.705 m) = 338.4 m/s λ3= 4/5 L3 = 4/5 (0.884 m) = 0.7072 m Hence the velocity v = fλ3 = 480 Hz (0.7072 m) = 339.456 m/s Hence the average velocity = 336.03 m/s LABORATORY REPORT Data Table 1 زرد C Speed of sound Room Temperature= 20.5 Data Table 3 Data Table 2 Hiz Frequency Fett Tm- 1020 Hz 17 Frequency Fork One = Loom) Loom) Ls (m) rn) L (m) را رد را 0.03 در 7 اور و 17 اور لا ارو 117 ورود زرار زرا اور در را در کار تار Calculations Table 2 / و=L در دمای را = ما = ما را * ا ر ا و ر ا =1 ارور = 1 = و = (یا۔ = (یا- پرلا (2=ية را17. = (ما- لا =ة = 77. = (ال2= ہر ا = 1 = ۷ ر ا ا = ر = 22 30 Calculations Table 3 = = 1 = 1 [2 = 0.lu کرا. را ر =L 242=0.0024 = = . =ة =رور == .ز= (یا-راد2=وة . = (یا- لا =ر 2 و را = = = = = ا / در مرد COPYRIGHT 208 Thomson Brooks Cole 1 = 1 - = ا -ي2= پر =) 231 th 232 Physics Laboratory Manual Loyd SAMPLE CALCULATIONS 1. Speed Sound=331.5 +0.607 T= 2. 22=2(L2-L)= 3. 12 =(L3-L)= 4. Az = 2/3(L4-L) 5. V = = 6. % Error = |E-K/K (100%) = QUESTIONS 1. What is the accuracy of each of your measurements of the speed of sound? State clearly the evidence for your answer. 2. What is the precision of each of your measurements of the speed of sound? State clearly the evidence for your answer. 3. Equations 2 provide a means to determine the end correction for the tube. Using the value of ī for the first tuning fork, calculate values for L, and L2 from those equations. They should be larger than the measured values of L1 and L2 by an amount equal to the end correction. Repeat the calculation for the second tuning fork. Compare these values for the end correction and comment on the consistency of the results. a rubber nding of mechanical, including photocopying, recording tapina Semarks used herein under license. ALL RIGHTS RESER e waves reflected from th cer. Standing waves are r hammer. end of the tube, el of the water the sound Laboratory 22 Speed of Sound-Resonance Tule 233 4. Suppose that the temperature had been 10°C higher than the value measured for the room tempe- rature. How much would that have changed the measured value of L2-L, for each tuning fork? Would L2-L be larger or smaller at this higher temperature? 5. Draw a figure showing the fifth resonance in a tube closed at one end. Show also how the length of the tube L5 is related to the wavelength 2.. Grein under license ALL RIGHTS RESERVED No part of this work of the tube, che water sound Ves reflected from the standing waves are rubber hammer. 1. recording taping web distribution normation 225
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