SOUND & MUSIC Sound is produced by a rapid variation in the average density or pressure of air molecules. We perceive sound as these pressure changes cause our eardrums to vibrate. Sound waves are produced by a vibrating object that causes a disturbance to the surrounding air molecules, causing them bounce off each other with a force proportional to the disturbance. The energy of their interaction creates ripples of more dense (higher pressure) to less dense (lower pressure) air molecules. When the molecules are pushed closer together it is called compression and when they are pulled apart, it is called rarefaction. The back and forth oscillation of pressure produces a sound waves. The sensations of these frequencies are commonly referred to as the pitch of a sound. A high pitch sound corresponds to a high frequency and a low pitch sound corresponds to a low frequency. A sound wave is a disturbance which travels through a medium (such as air). When one particle becomes disturbed, it exerts a force on the next adjacent particle, thus disturbing that particle 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. The speed of a sound wave in air deps upon the properties of the air, namely the temperature and the pressure. At normal atmospheric pressure, the temperature depence of the speed of a sound wave through air is approximated by the following equation where T is the temperature of the air in degrees Celsius. Speed (meters / second) = 331 m/s + [ (0.6 m/s/ o C)*T ] In dry air when the temperature is 0 o C, sound travels with a speed of 331. meters per second. When the temperature is not 0 o C, the speed of sound changes by about 0.60 m/s for each degree Celsius. For example, if the air temperature is 20.0 o C, the speed of sound would increase by a factor of [20.0 o C x 0.60 m/s/ o C] or 12.0 m/s; thus, sound would travel with a speed of (331. m/s + 12. m/s) or 343. m/s. PART I: SPEED OF SOUND WITH A BOOMWACKER Many woodwind instruments consist of an air column enclosed inside of a hollow metal tube. Though the metal tube may be more than a meter in length, it is often curved upon itself one or more times in order to conserve space. If the of the tube is uncovered such that the air at the of the tube can freely vibrate when the sound wave reaches it, then the is referred to as an open. If both s of the tube are uncovered or open, the musical instrument is said to contain an open- air column. A variety of instruments operate on the basis of open- air columns; examples include the brass instruments such as the flute and trombone and woodwinds such as the saxophone and clarinet. The basis for drawing the standing wave patterns for air columns is that antinodes will be present at any open and nodes will be present at any closed. If this principle is applied to open- air columns, then the pattern for the fundamental frequency (the lowest frequency and longest wavelength pattern) will have antinodes at the two open s and a single node in between. For Sound & Music 1
this reason, the standing wave pattern for the fundamental frequency (or first harmonic) for an open- and closed air column looks like the diagram below. open antinode node ½ wave antinode PROCEDURE: The purpose of this experiment is to compare the experimental frequency of an open and closeded tube with the theoretical frequency. To do this you will: 1) determine the speed of sound in air based on the temperature and 2) determine the wavelength of the vibrating column of air in the tube. Tap the Boomwhacker against your palm without the cap. This is an open-ed column. According to the diagram above, how much of a wave fits within the open-ed tube? open closed Place a cap on one and again tap the Boomwhacker tube. What do you notice about the change in pitch in the closed-ed column compared to the open ed column? node How much of a wave fits within the tube? ¼ wave antinode open SPEED OF SOUND IN AIR Record the air temperature. Determine the speed of sound in the room using the following equation: Speed = 331m/s + [ 0.6m/s/ o C x T ] EXPERIMENTAL FREQUENCY Using the speed of sound in air calculated above and the wave equation (speed = frequency x wavelength), determine the experimental frequency for two Boomwhacker tubes. Note Closed-Ended Tube Tube Length Wavelength Experimental Tube #1 Tube #2 Sound & Music 2
Open-Ended Tube Note Tube Length Wavelength Experimental Tube #1 Tube #2 Compare the experimental frequency with the theoretical frequencies from the table below by calculating the percentage error. Theoretical Frequencies Note Note Note Low C 131 A 220 F 349 D 147 B 245 G 392 E 165 Middle C 252 A 440 F 175 D 294 B 494 G 196 E 330 High C 512 Closed-Ended Tube Experimental Theoretical Tube #1 Tube #2 Percentage Error Percentage Error Experimental Open-Ended Tube Theoretical Percentage Error STATION #1: INTERFERENCE Sound waves interact with each other either constructively or destructively. When two crests or troughs combine the amplitude of the wave is increased and the sound becomes louder. When a crest and a trough combine, destructive interference causes the amplitude of the wave to decrease. The sound level is decreased. Tap the tuning fork with the mallet and rotate the tuning fork by your ear. What is the position is the tuning fork held when the sound is the loudest? Softest? How does the tuning fork destructively interfere the waves? Check this out at the oscilloscope. Sound & Music 3
STATION #2: BEATS Beats is a series of alternate reinforcements and cancellations produced by the interference of two sets of superimposed waves of different frequencies. This is heard as a throbbing effect in sound waves where there is an increase and decrease of the amplitude of the waves. Slightly adjust the metal clamps on the shorter fork up or down, this will change the frequency of the fork by a slight amount. Listen for the beat. Repeat the procedure by placing the microphone attached to the oscilloscope between the beat boxes. Now, whack each tuning fork. What do you notice about the waves which are produced on the screen of the oscilloscope? Follow the directions for using the signal generator. Construct a statement that connects what you see on the oscilloscope to what you are hearing. STATION #3: RESONANCE BOXES Resonance occurs when a vibrating object induces a forced vibration of another object. Using the two MATCHED forks, place the opening of one box several centimeters from the opening of the other box. Strike ONE of the forks. After a few seconds stop the forks vibrating by holding it. Listen at the opening of the other box. What caused the tuning fork in the second box to vibrate? Wind up the mechanical music box and hold it in your hand while it plays. Next, place the music box on the wooden resonance box. How does resonance apply to the change in loudness of the music box when placed on the wooden box? Sound & Music 4
STATION #4: RESONANCE TUBE Place the tube into the container of water as far as it will go. Strike the longer (lower frequency) tuning fork on the rubber wedge and hold the tuning fork over the open tube. Slowly raise the fork and tube together until the loudest sound is heard. You may have to repeat the procedure a couple of times to find the exact location. At the resonance point the tuning fork and column of air are vibrating at the same frequency so that an antinode (point of maximum expansion or rarefraction of air) of the wave forms at the open of the tube and a node (point of maximum compression of air) forms at the closed formed by the water. Repeat the experiment using the shorter (higher frequency) tuning fork. Of the two tuning forks which one resulted in a longer resonance point (longer wavelength)? STATION #5: PHYSICS OF MUSICAL INSTRUMENTS Play a note or a song on each of the musical instruments. Identify how each of these instruments produces sounds of different pitch and loudness. 1. Piano 2. Guitar 3. Slidewhistle 4. Xylophone Sound & Music 5
POST-LAB: BEATS SIMULATION Start the simulation produced by the Physics Department at Mt. Allison University. http://www.mta.ca/faculty/science/physics/suren/beats/beats.html The red and green waveforms can be manipulated by the slider bars at the bottom of the screen. Moving the slider to the right increases the frequency and moving the slider to the left decreases the frequency. The unit of frequency (oscillations / second) is Hertz (Hz), given in honor of physicist Heinrich Hertz. The waveforms can also be manipulated to be in phase and out of phase. SAME FREQUENCIES: Move the sliders for the red and green waves so that the frequencies are set at 10 Hz. The yellow waveform is the product of the interference of the two waves. What happens to the amplitude of the yellow wave when the red and green waves are in phase? Is this an example of constructive or destructive interference? If you could hear the resultant wave (yellow wave), how would it compare to the sounds of the red and green waves? Change the waves so that they are out of phase. What happens to the amplitude of the resultant wave? Is this an example of constructive or destructive interference. DIFFERENT FREQUENCIES: Make sure the waves are in phase. Increase the frequency of the red wave to 11 Hz by moving the slider slightly to the right. Notice the resultant (yellow) wave. What is the orientation of the crests and troughs of the red and green waves when the amplitude of the resultant wave is the greatest? What is the orientation of the crests and troughs of the red and green waves when the amplitude of the resultant wave is the least? If you could hear the resultant wave what would it sound like? Increase the frequency of the red wave to 12 Hz. How does increasing the difference in the frequencies of the two waves change the beat frequency in the resultant wave? Sound & Music 6