1. Lab 11: Standing Waves Only 1 more to go!! Wave: something that results from a disturbance and then travels away from that disturbance Example: Tossing a rock into a pond Important terms: Amplitude: how large or intense is the wave Frequency, f: how fast does the wave vibrates (oscillates) Wavelength, : distance between each successive identical points, such as the peaks

2. Wave Speed, v: how fast the wave propagates away from the disturbance v = f Two Types of Waves: Transverse: vibrations perpendicular to the wave direction (light waves, string waves) queen example Longitudinal: vibrations in the same direction as velocity (sound waves) backup example Interference: Constructive: occurs when the crest and troughs of two waves both occur at the same time + What if I asked you how far did the wave travel (in terms of wavelength) in one period? It turns out the frequency is related to period : f = 1 / T So substitute this back into our equation:

3. Interference: Destructive: occurs when the crest and troughs of two waves are perfectly out of phase + Standing Waves: If we choose the wavelength of the wave to be equal to the length of the string, the rebounding wave and incoming waves will constructively interfere. Antinode- regions of largest amplitude Node- regions of zero amplitude Antinode Nodes To have a standing wave the wavelength must equal with the length of the wave medium (string, air column)

4. For Strings: The first possible wavelength for a standing wave of length L must be:L = /2 This is the known as the fundamental frequency The next possibility will allow us to fit one more half wavelength: L = 2 / 2 For standing sound waves in an air column, there must be a node at the closed end and an antinode near the open end. L 1 = ¼ This is known as the first harmonic L L L 2 = ¾ L 3 =5/4 second harmonic second overtone L fundamental resonance first harmonic, first overtone

5. Today we will perform two experiments 1 st Standing waves in an air column: The position of the antinode does not exactly fit at the end of the tube. Through experiments we are able to find a more exact equation for the condition of the standing waves: L 1 + 0.4d = ¼ 1 st resonance L 2 + 0.4d = ¾ 2 nd resonance L 3 + 0.4d = 5/4 3 rd resonance You will measure L 1, L 2, and L 3 Then calculate the wave speed: v = f, find an average Compare with the theoretical speed of sound found by: V = 331.3 m/s + 0.6T (T is the temperature in Celsius)

6. 2 nd Standing Waves in a test tube Measure length of air column Find the frequency with the microphone Calculate 1/f Remember that the fundamental frequecy condition for a standing wave in a column of air is: L = /4and remember that v = f so = v/f if we substitute in for we get the fundamental frequency condition as being: If we plot L vs 1/f: L (meters) 1/f slope = v/4, so the speed of the wave will be: v = 4 * slope