2. Measure the rod's length and use it to determine the wavelength of the sound wave in the rod. The first photo gives you an overview of how the rod was measured. The second photo conrms that the end of the rod is lined up with the beginning of the metric ruler. The third photo is shown in expanded form to allow you to make a good measurement of how long the rod is. 2. Find the necessary constants from the chart below and calculate the speed of sound in that medium. Be careful with the scientic notation and exponents. The rod is made of aluminum. 3. Calculate the frequency of vibration (fwd) for the rod. This is your prediction. 4. Download a frequency meter to your phone. An example that works very well is the is the "Pano Tuner." available for free from the Apple App Store or the Google Play app store for Android. The icon looks like: '3 i'amrJTur'n-I 5. Listen to the standing waves produced by friction in the video. Place your computer near the microphone of your phone (it is near the charging port). Measure the frequency of the sound using the Pano Tuner or other app that you downloaded in the previous step. This is your experimental frequency fiexpl. 6. Compare the two values of frequency using percent difference. 7. Repeat this procedure for the second rod in the video. It is also aluminum and its length can be found in the following photos. \fLab Report - The Frequency of a Vibrating Metal Rod Name: Date: Objective: Data Tables Predicted Frequency: Rod L Y P V f (pred) Small Large Measured frequency and Comparison: Rod f(exp) % Diff Small LargeFrequency of a Metal Rod Instructions Objective: To predict the frequency of standing waves in a metal rod and the sound waves they produce. Materials: Cell Phone Apps Theory: Imagine dropping something and hearing the sound it makes as it hits the oor. Why does it make a noise with that particular pitch/frequency? We will answer that question for one particular object a metal rod. Standing waves in any medium produce, at certain frequencies, a large amplitude at the certain locations and zero amplitude at others. These are determined by the end conditions of the vibrating system. For example, a string tied at both ends must have nodes there. This means that waves for which multiples of onehalf wavelength fit onto the length of the string can produce standing waves, and only these waves. This yields the result that the harmonics are integer multiples of a fundamental. The waves traveling through the metal rod in our experiment are longitudinal waves, i.e.. sound waves. At the ends of the rod, the medium is not restrained from the in and out motion of the material. In fact. the medium is most free to vibrate there. So instead of there being nodes at the ends. we will have antinodes there. The simplest standing wave has antinodes (A) at both ends and a node [N] at the center. as in the diagram below. Since the distance between two antinodes is onehalf of the wavelength, the wavelength is twice the length of the rod: A = 2L. Since f = v/A, we have for the frequency of the fundamental of this rod _ L f _ 2L Actually. when an object drops and hits the oor. it will produce a set of frequencies simultaneously and a complex sound. The one we nd today [the fundamental} is only one of the possible standing waves in this set, but it is the easiest to produce and is the one we typically associate with the pitch we hear. The existence of a node at the center is helpful. Holding the rod at that location means that we will not dampen the wave the medium doesn't move there anyhow. Holding the rod at another position will dampen the wave quickly. We will need to know the velocity of the sound waves traveling through the metal rod to determine the frequency. The speed of sound through solids is given by the formula: _ i! 0 p where Y is Young's Modulus and p is the solid's density. Young's Modulus is a measure of how much force is necessary to stretch a material by a certain distance and so plays a similar role to the spring constant k. It tells us essentially how "springy" the material is. Its units are Pa = N/mz, the same as for pressure. The density is a measure of inertia with units kg/m3. Knowing these two constants will allow us to calculate the speed of sound in that medium. Knowing v {from that calculation} and L (from a measurement of the rod], we can predict the frequency of the fundamental in the metal rod