_Lab 4 Worksheet.docx

Phys1011: Sound Intensity Level and Sound Intensity (Week 4 Lab) Name: Gianna DelMonte Date: 10/04/2023 Instructor: Ms. Tenny Please view the Week 4 Lab video for instructions to fill out the worksheet. You may either type your answers to questions in the worksheet, or insert digital pictures of hand-written work in the appropriate places. The purpose of this lab is to determine relationships between the sound intensity level, sound intensity, and distance away from a source. This lab will require you to use a tone generator from a computer, laptop or mobile device other than one you will be recording the sound on. If you are unable to use a computer, laptop, or a secondary mobile device to produce sound, and a mobile phone or device to record sound, an alternate method is provided using your IOLab unit and laptop or computer that you normally use for this course. There are several online tone generator programs available for free. One that I prefer to use is: http://www.szynalski.com/tone-generator/ . You are welcome to use other sites, as long as they can produce a constant tone at a set frequency. For my example, I used 440 Hz. Download a free microphone app (application) capable of measuring sound intensity level to your smartphone or other mobile device that has a microphone. A reminder, this device cannot be the same device that is being used to generate the tone. The app can be any type of free or paid meter, as long as it can measure Sound Intensity Level in decibels. Two that work well are: ● Decibel 10: Noise dB Meter, FFT Frequency Analyzer by SkyPaw Co. Ltd. (Apple iPhone, iTunes Store) ● Sound Meter by Smart Tools Co. (Android) You will also need a ruler to tape measure to mark off equal distances away from your computer speaker or other sound source. My recommendation of distances are every 5 cm from 5 cm to 35 cm (requirement: at least 7 measurements, equally spaced apart, starting a few cm away from your source).

Part 1 – Measuring Sound Intensity Level 1. Watch the lab video. Play a tone from your ‘source’ computer, laptop, or mobile device. Take a digital picture of your sound source along a piece of paper including your name, date, and lab number (similar to previous labs). The tone from my source was set to 440 Hz. 2. Using the mobile phone or device, record the sound intensity level (in decibels, dB) for several seconds at a fixed distance away from the source. Record the observed value. If the value fluctuates, record an average value or a median (approximate middle) value for the time period. Record your observations in a data table in Excel. An example start of a table is provided below. Record at least seven at most ten sound intensity levels at different distances away from the source. (Table 1. Example data table with distance from source in meters and sound intensity level in decibels.

Part 2 – Sound Intensity versus Distance 4. Add a column to the right of the sound intensity level in your table. From the lab video and your textbook, determine the intensity of each sound intensity level in W/m 2 . You may assume that the reference intensity, I 0 is 10 -12 W/m 2 . An example is provided below (Table 2): Table 2. Addition column with sound intensity in W/m2. Include your table below. 5. How are sound intensity and distance from the source related? We will answer this through graphical methods. Linearization is a tool used to examine relationship between variables. We strive to find linear relations and easy to understand models to capture relationships between dependent and independent variables. Make a quick plot of distance from the source and intensity. Is it linear? If so, this is an easy direct relationship, and we are done. But this is likely not the case. If it is, you may need to look at your data or calculations again. Regardless, we should look at other relationships to determine which one is the most linear fit.

For simplicity, let’s call the distance from the source (in meters), R. Let’s call the intensity (in W/m2), I. I (y-axis) vs. R (x-axis) is not quite linear. Instead of plotting I vs. R, we can try variations of R. For example, you can try: I vs. 1/R I vs. 1/R 2 I vs. R 2 6. Write a hypothesis about which relationship will be linear. I hypothesize the I vs. 1/R graph will produce a linear relationship. I believe this because the two variables share an inverse relationship. As the x-axis or independent variable increases the y-axis or dependent variable decreases. As distance increases the intensity of the sound decreases. By taking the reciprocal of the distance values you can linearize the graph against intensity. Produce three graphs from your data to support claims (one graph per possible relationship from above), and explain the relationship between the claim and evidence. It may help to make a new data table to produce these graphs. An example is provided below in Table 3.

Graph I vs. 1/R 2 Graph I vs. R 2

7. Which relationship is linear? After producing all three graphs from the data I collected, I believe the I vs. 1/R graph is the most linear graph. Most sound sources are considered point sources, and sound will spread spherically away from the source in the air. Consider the surface area of a sphere. What is the formula for the surface area of a sphere? If you don’t remember this, please look this up on the internet or in the reference section of your textbook. How does this explain the intensity of sound as you move away from a point source? The formula for the surface area of a sphere is A = 4 π r 2 . If sound moves spherically away from a point source then the radius increases as you move away from the sound. As you move away from the source of a sound and the radius increases the area increases as well. For example, with a radius of 5, the area is equal to 314.16. As the radius increases to 10, the area increases to 1256.64. The spherical area that the sound reaches increases as you move away from the point source. The intensity of the sound is spread over a larger area as you move farther away and so the intensity and pitch decrease. Math Calculations: A = 4 π 5 2 = 4 π (25) = 314.16 A = 4 π 10 2 = 4 π (100) = 1256.64 8. Power of a sound wave is related to the intensity and the surface area of the wave. From your data table, provide an estimate of the power of your sound wave (in Watts, W) for one fixed distance, R (in meters, m) away from the point source. You will need the surface area of a sphere. Look at the last slide in the Week 3 material if you have any questions on this calculation. For this calculation, I chose to use the intensity value calculated at 0.25 m away from the source of the sound. Using the distance of 0.25 m as the radius I was able to calculate the area of the sound. By multiplying the area and the intensity I was able to calculate the power in watts as 6.24 * 10 -6 W. I = 7.94 * 10 -6 radius/distance from source = 0.25 m A = 4 π r 2 P = ? I = P / A 7.94 * 10 -6 = P / 4 π (0.25) 2 7.94 * 10 -6 = P / 0.785 (0.785) 7.94 * 10 -6 = P / 0.785 (0.785)