Lab #13 Speed of Sound Purpose The purpose of this lab is to explore resonance to calculate the speed of sound in air Introduction A wave is a disturbance that travels through a medium, transporting energy from one location to another. Wave energy can be classified as mechanical or electromagnetic. Mechanical waves require particle interactions for movement and only occur in particulate media such as air, water, and solids. Examples of mechanical waves include sound, seismic, and ocean waves. Electromagnetic waves do not require particle interactions for movement and occur in both particulate media and vacuums. Examples of electromagnetic waves include visible light, radio, and microwaves. Mechanical waves propagate (move) in two ways: transversely and longitudinally. When transverse waves propagate, the particles of the medium move in a perpendicular direction to the flow of energy (the direction the wave moves). Transverse mechanical waves occur in solid media and on the surface of liquids. Conversely, the propagation of longitudinal waves results in the parallel movement of particles in the medium in relation to the flow of energy. Longitudinal waves occur in air, liquid, and solid media. See Figure 1 for an illustration of mechanical waves using two springs. The energy in each spring flows from right to left. The particle interactions of the upper spring create a transverse wave by moving perpendicular (up and down) to the flow of energy. The particle interactions of the lower spring create a longitudinal wave by moving parallel (back and forth) to the flow of energy. Hand motion Transverse Waves Wave direction Compression Rarefaction d motion Longitudinal Waves Figure 1 Transverse and Longitudinal Waves Copyright 2007 - 2020 Revision World Networks Ltd. A vibrating surface in air will set up a series of increased pressures (compressions), followed by decreased pressures (rarefactions), which will radiate outward from the vibrating source. A series of longitudinal waves may be represented as seen in Figure 2 below: Figure 2 Compressions and Rarefactions in a Transverse WaveThe close spacing of the lines represents increased pressure and the greater spacing represents decreased pressure. The individual particles of the medium through which the wave is travelling will vibrate back and forth in the direction of the wave. The displacement from their equilibrium position in the medium may be shown in Figure 3 below: A Amplitude Mean Level Wavelength Figure 3 Transverse Wave on a string Standing Waves and Resonance Wave interference occurs when two waves occupy the same position at the same time. The superposition principle is used to determine the result of two or more waves interfering. Figure 4 below shows two examples of interference. Destructive interference of two pulses constructive interference Figure 4 Destructive and Constructive interference. Figure 4 above illustrates constructive and destructive interference. The left side illustrates destructive interference (when two pulses cancel each other out) and the right side illustrates constructive interference (when the two pulses combine to create a single greater amplitude pulse). In Figure 4 both examples start with two pulse waves traveling toward each other. On the left, the two pulses are inverted from each other (one peak is up, the other is down). On the right side the two pulses are pulsed in the same direction (both peaks are up). If you look at the lines from top to bottom you are looking at a different snapshot in time as the two peaks travel towards each, cross each other and then continue traveling in the opposite direction. Purely destructive interference occurs when two waves arrive at the same location at the same time with amplitudes in the opposite direction (out of phase). When this happens the waves cancel each other out. The middle line on the left side of Figure 4 shows the result of purely destructive interference. Purely constructive interference occurs when two waves arrive at the same location at the same time with amplitudes in the same direction (in phase). When this happens the two waves add to each other and create a single greater amplitude wave. Since most waves are not single pulses, they can combine in many combinations from purely constructive to purely destructive and everything in between.When a string is attached to a vibrating source on one end, and a fixed point at the opposite end it is possible to create something known as a standing wave. If you create one short pulse at the vibrating end, this pulse moves along the string toward the fixed end. When the pulse hits the fixed end it inverts and returns toward the vibrating end. If you send multiple pulses out from the vibrating end, each will travel down the length of the string to the fixed end, invert and travel back to the vibrating end. If the pulsing is done at certain specific frequencies the outgoing and incoming pulses will interfere in such a way as to create a standing wave. You will explore this in the simulation portion of the lab below. The points on the string where the two waves arrive out of phase destructively interfere and create a point of little or no energy. These points are called nodes. (See Figure 5 below). At other points along the string the two waves arrive in phase and they constructively interfere creating a point of maximum amplitude (double the initial amplitude of the original wave). These points are called antinodes. eling Waves Standing Waves Figure 5 Traveling and Standing Waves Resonance is the amplified sound produced when a one vibrating object forces a second object into vibrational motion. This phenomenon can be observed on a violin when one string's motion causes another string to vibrate. Have you ever heard about singers breaking a wine glass with only their voice? That's resonance. The singer simply needs to find the natural frequency of the glass (tap on it and listen to its sound), then sing at that frequency loud enough and it will break. Resonance is produced as waves of identical frequencies traveling in opposite directions meet, resulting in an interference known as a standing wave. Standing waves appear to be stationary. See Figure 5. For this lab you will create a sound wave using a tuning fork. The tuning fork can cause the air column in a tube to vibrate at that frequency as well. This is called resonance, the air resonates at the frequency of the tuning fork. If a tuning fork is held over an air column in a closed tube, compressions and rarefactions will travel down the tube and be reflected. If the tube length is adjusted until it is equal to exactly one-fourth the wavelength of the tone from the fork, the returning wave will arrive back at the top of the tube in phase (constructively interfere) with the next vibration of the fork, and a tone of unusually loud volume will be heard. This phenomenon is known as resonance, and it occurs when standing waves are set up in the tube with a node at the closed end (water level) and an antinode (constructive interference) very near the open end. This situation can occur when the length of the tube is any odd number of quarter wavelengths of the sound waves being emitted by the fork. (See the Figure 6 below). Resonance will occur whenever the length of the air column in the tube is: 2/4, 32/4, 52/4, ...(2n+1)2/4 where n is an integerTuning Forks 1/4 Wavelength Water 3/4 Wavelength Resonance Tubes - Wate Figure 6 Standing Waves in a Tube The fundamental equation of wave motion is v = fa where v = speed of propagation of the wave f = frequency 2 = wavelength Since the frequency of the fork is known and 2 can be calculated from measurements taken at a point of resonance, the speed of sound in air can be calculated. The speed of a sound wave through air is only dependent upon temperature and may be closely approximated by the following equation. Vtheoretical = Vo + 0.6T where vo = 331 m/s speed of sound in air at OC at normal air pressure T = Temperature of the air (room temperature in degrees Celsius) theoretical = theoretical speed of sound in air at room temperature The Step by Step procedures for this lab are on the remaining pages below.Procedure: Experiment Data collection Use the thermometer to measure the temperature of the room and record in Data Table 1. WN- Fill a pitcher or tall vase with enough room temperature tap water to submerge at least 80% of the length of the pipe. Use the inner jaws of the Vernier Caliper to measure the inside diameter of the plastic pipe and record to 0.01 mm in Data Table 1. Refer to Lab 3 Measurements for directions on how to use the Vernier Caliper. Convert the mm to m using the conversion factor 1 m = 1000mm. and record with the correct number of sig fig in Data Table 1. (Use the increase or decrease decimal button if needed). 4 . Place the plastic pipe into the pitcher of water to create a resonance tube. The water level creates the fixed end. U Examine the tuning fork and record the imprinted frequency in Data Table 1 in Hz. Grasp the tuning fork by the handle and strike the opposite end against a rigid, unbreakable object such as a piece of wood or rubber shoe sole. Na Immediately place the vibrating tuning fork over the opening of the resonance tube, (see Figure 6) being careful not to touch the tube with the tuning fork. 8. While maintaining the position of the tuning fork over the tube, raise the tube to lengthen the air column until you can hear a louder resonance tone. This should be a clear sound. To help you find the tone, you can relatively quickly raise and lower the tube while holding the tuning fork above it. Once you hear the resonance you can fine tune the location using the steps below. Hint it should be when the tube has a large portion out of the water. 9. Upon resonating, carefully adjust the height of the tube until the loudest sound is produced. Note the approximate location on the resonance tube. Remove the tube from the water. With a pencil, make two to three lines to lightly mark the pipe in a few locations above and below the position you noted on the pipe. This will help you better determine the exact location of the resonance. Figure 7 Sample Markings 11. Repeat steps 6-10 to make additional markings between the existing markings above and below the location of the position found in step 10. 12. Repeat steps 6-11 until you can precisely measure the position of the resonance on the tube. 13. Use the ruler to measure the length of the air column and record as Trial 1 to 0.01 cm in Data Table 2. 14. Repeat steps 6-13 for two additional trials, recording the lengths as Trial 2 and Trial 3 in Data Table 2. 15. Convert the Trial length in cm to m using the conversion factor I'm = 100 cm using the correct number of sig fig. 16. Calculate the mean length from the three trials and record in Data Table 2 17. Use the equation 1 = 4(L + 0.3 d) and the mean length to determine the wavelength of the resonance. Record in Data Table 2.18. Use the equation v = af to determine the speed of sound in the air column and record in Data Table 2. 19 . Calculate the theoretical speed of sound at your experimental air temperature using the equation: Vtheoretical = Vo + 0.6T where vo = 331 m/s (speed of sound in air at 0 C at normal air pressure) T = Temperature of the air (room temperature in .C) Vtheoretical = theoretical speed of sound in air at room temperature 20. Calculate the percent error between your experimental results and the theoretical speed of sound using the equation percent error = Vtheoretical - Vexperimental x 100% Vtheoretical and record in Data Table 2. 21. The resonance tube used in this experiment produced only one resonance tone. Calculate the minimum length of tube needed to produce a second tone under the same experimental conditions. Use resonance locations from the background information to assist you in calculating the length needed. Keep in mind you found the location of the first resonance. 22. How would your calculations for the wavelength and speed of sound recorded in Data Table 2 vary if a 512 Hz tuning fork were used? Use the dropdown arrows to select your answers. 23. Return all HOL supplied materials to the lab kit.Procedure: Exp Data Collection Data Table 1 Inner Diameter Temperature (C) (mm) (m) Frequency (Hz) 21 C 20 0.02 384 Data Table 2 Length (cm) Length (m) Mean Length (m) wavelength |speed (m/s) Trial 1 21.00 0.2100 Trail 2 21.50 0.2150 Trail 3 22.00 0.2200 V theoretical Percent Error Within 10% Minimum length for second resonance How would your calculations change for the following if you use a 512 Hz tuning fork instead? Wavelength? Speed of sound