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Homework answers / question archive / Lab 05 Speed of sound and standing waves Physics 4C 9 May 2021 revision Physics 4C Lab 05 Speed of Sound and Wavelength in Air Ref: Standing waves, Serway Section 18
Lab 05 Speed of sound and standing waves Physics 4C 9 May 2021 revision Physics 4C Lab 05 Speed of Sound and Wavelength in Air Ref: Standing waves, Serway Section 18.5 Background and Introduction In the past this Laboratory Experiment was done with a tube, a tall beaker of water that had a mechanism for adjusting the water level of the beaker, and a tuning fork as a sound source. At home we don’t have the convenient way of rapidly changing the water level. There were a limited number of tuning fork frequencies and the volume was relatively low. The sound amplitude tended to have a rapid decay time so students needed to re-strike the tuning fork frequently. In our modern era we can replace the tuning fork with a tone generator in a phone. (In earlier execises we downloaded PhyPhox so that that app needs no further explanation.). The phone with its high volume provides a substantial improvement over tuning forks. PhyPhox tone generator on Android. Frequency can be selected between 100 and 8,000 Hz. The speaker for this phone is the horizontal line located at the top. The tone frequency can be set by adjusting the settings. When active the display shows a graphic representation of the tone graphically with amplitude vs time. Procedure. Find a suitable tube of about 0.3 meters in length. Copper pipe, steel pipe and plastic can be used. In the example shown here ¾ inch PVC (a type of plastic) tubing was used. This can be purchased at almost any hardware store. Most store owners will cut it to length for you, just ask. Don’t be afraid of asking in a store! If you don’t have a store, you can build one yourself from paper and lots of transparent tape. The tube is immersed in water so is should have some water resistance. See the photos at the end of this document. 1 Lab 05 Speed of sound and standing waves Physics 4C 9 May 2021 revision Attach a length scale to the tube. Here a 1 cm by 1 cm grid was downloaded from the web. Cut a strip that can fit along the tube, mark it with the numerical scale and seal it on all sides with transparent tape so that it is waterproof. Find a method of positioning the phone to the top of the tube so that you can use your hands to lift the cylinder that holds the water. Be cautious! My printer shrinks the grid scale slightly. A re-calibration of the scale units is necessary ( mine: 20 units = 19.0 cm, what are yours? Materials: ¾ inch PVC tube (available from any hardware store. The scale is created by printing a 1 cm x 1 cm grid paper, cutting out a strip and indicating centimeter distances. Attach the marked striped with transparent tape so keep the paper dry when submerged in water. The water level is provided with a tall water bottle. The red bottle shown was a hand-out to all students from Foothill. The tube is attached with a rubber band to a flexible piece of plastic (or any other material) to hold the tube vertically with the top near the table edge. The phone is placed face-down with the speaker pointing down the length of the tube. The speed of sound is related to frequency and wavelength ? = f*?? where ? is the sound speed and ? is the wavelength. Lab activity: First locate the speaker of your phone. Set some frequency on the tone generator in the phone. Place the speaker of the phone a short distance above the open top of the vertical tube so that the sound from the phone is projected into the tube. Next raise the water level that closes of the end of the tube by lifting the bottle until a distinct resonance, i.e., an increase in the tone volume (amplitude) is heard. Record the distance on the scale between the water level and the 0 marker on the tube. Repeat this for three different frequencies of your choice, but separate them widely in frequency. 2 Lab 05 Speed of sound and standing waves Physics 4C 9 May 2021 revision The distance between the speaker and the water level, i.e., the length of the tube, is ¼ of a wavelength (?) There is another resonance at ¾? and onward… Record the distance between the speaker and the water level when you hear a resonance in a table. For most of your measurements at higher frequencies measure 1/4?? ¾?? .and if possible 5/4 ?? Procedure: 1. Measure the room temperature in degrees Celsius and calculate the theoretical speed of sound. 2. Fill the plastic container with water and insert the tube into the container. start with an air column of about 3cm if possible. You should start with a air column as short as possible. The length of the air column is measured from the top of the tube to the water surface. 3. Start your cell phone app, measure the audible range of frequency for your phone and your hearing. 4. With a frequency of at least 1000 Hz. Hold your cell phone speaker above the tube. Slowly move your plastic tube upward. The length of the air column increases as you move the tube upwards. Listen for the resonance to occur (you will hear the loudest sound). The length of the air column when you hear the first resonance is marked as L . Make a few trials to make sure that L is correct. You can use the smaller beaker to adjust the water level. You may need to adjust the speaker’s position until you get the optimal effect. 1 1 5. Repeat step 2 to determine the second resonance, then third, fourth, fifth …. etc resonances until the bottom of the tube is above the water surface. Record the resonances positions as L and L , L , and so forth. You will measure few positions at low frequency (near 1000 Hz), more positions at high frequency. 2 3 4 6. Repeat step 4 and 5 for a total of four frequencies. The frequency range is from 1000 Hz up to the highest frequency that is near the maximum that is audible to you. 7. Calculate the λ and multiply the frequencies to determine the speed of sound and compare with the theoretical value. Find the percentage error. Data to be recorded: Record the following measurements in your lab report. Be sure to use heading and your name. Do the lab yourself with your own apparatus. Temperature( C): 0 Vtheory: (see the formula above) 1.) Record the audible range of frequency for your phone and hearing (lowest frequency, highest frequency): 3 Lab 05 Speed of sound and standing waves Physics 4C 9 May 2021 revision 2.) Follow the procedure to record data in steps 4,5,and 6. The L1, L2 below indicate the distance between the speaker and the water level for the first, second, third resonance. Do this for four frequencies from low to high. You might not be able to find higher order resonances for lower frequencies. 1 Data Table for report 2 4 3 option Frequency (Hz) L1(meters) L2(m) L3(m) L4(m) L5(m) L6(m) L2-L1 L3-L2 L4-L3 L5-L4 L6-L5 ΔL average λaverage (m)= ΔL x2 avg v (m/s) For your Lab Report. Do Not copy all of the lab procedure. Instead describe how YOU did the experiment. Include one or more photographs of your tube and water container. If you have a second camera show these with your phone. Comment on the uncertainty of the length measurements. Comment if you heard any sounds at intermediate points. How did the actual measurement process differ from the simple textbook expectations? Use Your Data to calculate the speed of sound. Average of v (experiments): percentage error: Write only significant digits consistent with your measurements. 4 Lab 05 Speed of sound and standing waves Physics 4C 9 May 2021 revision Questions: 1. Sketch the standing wave pattern of the fourth resonance position. 2. Does changing the water level change the wavelength of the wave? Explain. 3. Why are the resonance positions different when different frequency was used? 4. Comment on sources of errors. Experimental note: Textbooks picture the wave amplitude having a maximum right at the opening of the tube. This is incorrect by a small but measureable amount. This will affect the measurement of the first resonance ?1/4 ? Additional work for top grade: RESONANCE WIDTH. For a given driving frequency you hear the sound intensity rise and fall as you change the water level and therefore the length of the tube. This peak is called a “resonance”. The concept of resonance is essential to almost all of physics research, but also mechanical engineering, electrical and optical engineering and medicine (For fun learn about Ultrasonic Diagnosis). We can characterize the resonance by its fundamental frequency and also by its width. One (of several) ways of describing a resonance width is by Full Width at Half Maximum (FWHM). For one frequency but at least three resonances, record the length L when the sound level is at maximum, then measure the length when the sound intensity is half that of the sound level at the peak. THIS is approximate, but make your best estimate. The concept of resonance widthis very important. The figure from Wikipedia provides the idea of FWHM. The figure is for frequency, but we will use tube length. Basically we ask, is the resonance wide or narrow. A more advanced question here is how wide is the resonance compared with the distance between two resonances? Wikipedia Sound Resonance https://en.wikipedia.org/wiki/Acoustic_resonance ------------‘ End ----------------------. 5 Lab 05 Speed of sound and standing waves Physics 4C 9 May 2021 revision Note for a homemade tube. Addition for those who couldn’t find a hardware store. I rolled a piece of standard letter paper, then covered that with transparent tape (like Scotch), then rolled a second piece of paper around that, and covered that with tape. The tape is to add some degree of water resistance. Do this with several papers to make the tube somewhat rigid. The last piece should be marked with a scale of some sort to assist with measurement. Then cover that with tape. Find a way to hold the tube relative to the phone without using your hands. E.g, it might be a piece of string or a piece of flexible plastic with a rubber band. Paper tube with phone. The can serves as a weight on top of a piece of plastic that is attached with a rubber band to the paper tube. Paper tube with several layers of paper and tape. Verify the scale you use with a ruler. Some printers stretch or shrink the spacing. 6 Lab 05 Speed of sound and standing waves Physics 4C 9 May 2021 revision -----------------------Lab Instruction for On-Campus Lab----------------. This is provided for background information. Lab Speed of Sound in Air (at home) Purpose: To measure the speed of sound in air by determining the wavelength of resonant sound waves in an air column with variable length. Background: Sound waves are longitudinal waves traveling through an elastic medium. The source of sound waves is a vibrating object such as a loudspeaker or a tuning fork. The air in the path of the sound wave becomes alternately denser and rarer. When the molecules are forced closer together than normal, the region of higher density and air pressure is called a compression or condensation. When the molecules are spread farther apart than normal, the region of lower density is called a rarefaction. The speed of sound in a gas varies linearly with its temperature. For sound wave travel through air, the speed and medium temperature are related by V = 331*(1 + Tc/273)1/2 m/sec V is the velocity of sound, Tc is the temperature of the gas (here it is air) in C. When a sound source vibrates at the open end of a tube with one closed end, air waves will be sent down the column of air in the tube. These waves will be reflected with an 180 phase change when they strike the water surface at the closed end of the tube. Due to superposition, the reflected wave and the wave sent down the column will form a standing wave. The frequency of the traveling sound wave is the same as the frequency of the tuning fork, the traveling wave and the reflected wave combine may form a standing wave of the same frequency. When a standing wave is formed, a loud sound is produced, this is called resonance. Since the speed of sound in air and the frequency of the tuning fork are constant, the wavelength of the sound wave of the tuning fork is constant. Changing the length of the air column allows standing waves of higher harmonic to be formed. With the tube open at one end and closed at the other, only standing wave with a node at the closed end and an anti-node at the open end will form. You will hear a o 7 Lab 05 Speed of sound and standing waves Physics 4C 9 May 2021 revision loud sound when the condition to form a standing wave is satisfied; the standing wave in the tube resonates with the incident wave of the tuning fork. The first resonance has the smallest air column L , and corresponds to a standing wave of one quarter of a wavelength, giving L = ¼λ. The air column for the second resonance will have L = 3/4 λ. We see that the difference between the air column lengths at the first and second resonance position is ½ λ. So the wavelength of sound wave in air can be determined by λ = 2(L – L ). Once we know the value of λ, we can use the frequency of your tuning fork to determine the speed of sound in air: v = f λ. 1 1 2 2 1 8
