Physics 248 Spring 2009

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1 Physics 248 Spring 2009 Lab 1: Transverse standing waves on a string and speed of sound in air Your TA will use this sheet to score your lab. It is to be turned in at the end of the lab. You must use complete sentences and clearly explain your reasoning to receive full credit. SC-1 Transverse Standing Waves on a String PART I: Waves from a speaker 1. We are studying standing waves on a string that is fixed at two ends. Remember that in class we said that there are specific values of the frequency at which the string resonates. What is the general expression for these frequencies? 2. Observe Fig. 1 in the lab manual: how many nodes you should see for the first harmonic, the second harmonic and the third one? During the experiment try to see these features helping yourself with a white piece of paper. 3. What is the separation between nodes and antinodes? 4. Measure the value of the string mass per unit length and write it down here.

2 µ 5. Calculate the necessary string tension to produce a standing wave in the first, second and third mode when the applied frequency is 60 Hz. T 1 T 2 T 3 6. Considered that the hanger itself has a mass of 50 g. What are the masses that you would need to put on it to get these tension values? 7. Verify that you see the second and third resonant modes on the string for values of the masses on the hanger close to the ones you calculated. How do the values of the masses for which you

3 see the resonant modes on the string compare to the calculated values? 8. Follow the instructions in your manual for points from 5. to 9 putting a mass of 200 g on the hanger. Record below the second mode frequency f 2 and the third mode frequency f 3 you find. f 2 f 3 A few recommendations: - Try to have a string length L not less than 1.4m. Notice from the manual figure from what point to what other you have to measure it. - have the string touch the bridge to have the second end of the string fixed

4 - do not trust the value given in the manual of the mass of the string per unit length, measure it after you cut the piece you need weighting it and measuring its length. PART B: Not needed. Go ahead with the second experiment S-2.

5 S-2: Velocity of Sound in Air with a resonant tube In this experiment you will observe the resonance phenomenon in an open ended cylindrical tube and you will use the resonance to determine the velocity of sound in air at room temperature. As you know from lectures, the velocity of a sound wave in any medium can be determined if the frequency and wavelength are known. The apparatus is a long cylindrical plastic tube attached to a water reservoir. You can vary the water column by raising or lowering the water level while the tuning fork is held at the open end of the tube. Resonance is indicated by the sudden increase in intensity of the sound you can produce striking the fork with the rubber mallet when the column is adjusted to the proper length. The resonance is due to a standing wave phenomenon similar to the one that happens in a string free at one end. The water surface is a node of the standing wave since the air is not free to move longitudinally. The open end provides the conditions for an antinode. 1. Write the relationship between velocity, frequency and wavelength.

6 2. Read the value of the frequency on the tuning fork. f fork 3.. At what values of the lengths of the water column do you expect to have the first three resonant modes? Express this as a function of the wavelength of the sound wave. 4. Measure the values of the lengths of the water column for the first three resonant modes. Initially have enough water that you can raise the level above the first resonance position. L 1 L 2 L 3

7 5. Then calculate the velocity of sound for the 3 values above and calculate their mean value, the sample standard deviation and the standard deviation of the mean: v = "," = N " mean = ". How accurate is your measurement? N N i=1 v i N $ i=1 (v i # v) 2 N #1 and v 1 v 2 v 3 v mean ± σ mean Accuracy of the measurement = 6. The speed of sound depends on the temperature. Calculate the value of the speed of sound at T = 0 o C = o K applying a correction to the value you measured at the temperature of your lab. Remember that v = "RT M, where the molar mass of the gas for air is M air 29 x 10-3 kg/mol), R is the universal gas constant = J/(mol o K) and γ air = 7/5. Compare your measured value to the accepted value for dry air at 0 o C that

8 you can find out in 7. What is the effect of humidity on your measurement? Check it from the calculator above.

Sound. Measure the speed of sound in air by means of resonance in a tube; Measure the speed of sound in a metal rod using Kundt s tube.

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