Homelab 5
Step 1 The first step is to assemble your panpipe tube. You should have a piece of plastic pipe that is about 20 cm long, a small ball of clay, and a wooden plug that fits loosely inside your tube. The pipes we gave out in class are made of a plastic called CPVC and they have a inside diameter of about 1.2 cm. It will help to have one or two unsharpened pencils on hand, or pencils with unused erasers. First, make a ball of clay with a diameter a little less than the inside diameter of your tube. Then slip the ball of clay into the tube, and put the wood plug in after it. Hold the tube upright (as shown in the drawing), and use a pencil or something else to keep the plug from slipping out. Put the square end or eraser end of a pencil in from the top, and pack the clay in so it makes a flat floor that completely seals the tube. To check that the tube is sealed, put your lips around the top and blow gently. Carefully measure the inside length of the tube L. This can be done by putting a pencil into the tube (square end first) until it touches the clay, marking the depth on the side of the pencil, and then removing the pencil and measuring it with a ruler. If you only have an inch ruler you should measure the length in inches and then convert to centimeters, using 1 inch = 2.54 cm. Measure as accurately as you can. For L to be well-defined it is important that the floor of the tube should be flat.
Step 2 Learn how to play your panpipe tube. Hold the tube vertically and place the open end at the bottom edge of your lower lip, then direct a steady stream of air towards the back edge of the tube. This YouTube video, shows the technique. When you can produce a steady tone, you will notice that the pitch can be lowered by covering more of the tube with your lower lip, or by blowing more directly into the tube. For this lab try to get the highest pitch you can from the fundamental mode. It is not necessary to play the tube with the excellent tone quality that the player in the video demonstrates. If you can hear some hint of the tone, that will be enough for this homelab.
Step 3 Measure the frequency of the fundamental mode using Raven Light. As in the previous homelabs, make a recording and then adjust the focus and other controls so you can make the most accurate measurement possible. (It is difficult to 'overblow' the tube and excite the second or higher modes, so you probably wont have any trouble getting the right mode.) Measure the frequency for three different values of the length L ranging from something close to the full length of the tube to about half the full length. (Be careful you don't blow into the wrong end of the tube.) It does not matter exactly what lengths you use as long as you measure them accurately. Find the periods T that correspond to each frequency and convert the lengths to centimeters if you measured them in another unit.
Step 4 Make a graph of your results on this form. Plot the tube length in centimeters on the x-axis and the period T in milliseconds on the y-axis. Start both axes at the point (0,0) at the lower left corner of the graph. Label both axes clearly.
Step 5 The frequency of the fundamental mode of a pipe closed at one end is f = v/(4*L), where v is the sound velocity. You can rewrite this equation as T = (4*L)/v, where T is the period. This equation predicts a linear relationship between L and T. Draw the best straight line you can through your three data points, but do not force your line to go through the point (0,0). The effective acoustic length of your tube is a bit longer than the length you measured because of the 'end correction' at the open end. Because of this effect, your line should cross the x-axis at a small negative value of x.
Step 6 Another way to write the formula for the fundamental mode frequency is like this: v = (4*L)/T. You could use this form directly to measure the sound velocity. However, because of the end correction mentioned above, it is more accurate to measure the sound velocity using the change of T as you change L, rather than the absolute values of T and L. With a little algebra you can derive this formula: v = (4*dL)/dT. Here dL=L1-L2 is the difference between your longest length and your shortest length, and dT=T1-T2 is the difference between your longest period and your shortest period. Use this method to measure the sound velocity, and write your result clearly on your graph.
Step 7 Scan your homelab to a pdf file using a scanner or a smartphone app, and upload it to the dropbox on our Canvas site before it is due.