Lesson+27+&+28

**Advancememt in Physics @ Dwight Englewood** **Director: Elise Burns** **TA: Sebastian Loh**

Standing waves a pattern created by interference of travelin waves due to resonanance no crests and trof there are nods and anti nodes Resonanace when thenatural frequency of an object is reinforced by an external object causinga standing wave to form.

Length of a wave length = n1/2 wavelength

**Purpose:** To determine the relationship between the number of harmonics, the frequency of the source, and the wavelength of transverse waves traveling in a stretched string. **Materials:** Electrically driven oscillator; pulley & table clamp assembly; weight holder & selection of slotted masses; black Dacron string;

**Procedure:**

 * 1) Set the frequency of the oscillator to zero. Set the amplitude to maximum.
 * 2) Measure the length L of the string.
 * 3) Dial up the frequency a little at a time until you acquire a standing wave. If you are careful, you should be able to get the fundamental. However, if you don’t, it’s okay… just record the correct number of antinodes along with the frequency.
 * 4) Measure the wavelength.
 * 5) Repeat for at least 7 different harmonics. These do not have to be consecutive.

<span style="color: #ff0044; font-family: Tahoma,Geneva,sans-serif; font-size: 110%;">**Data / Chart :**




<span style="color: #ff0044; font-family: Tahoma,Geneva,sans-serif; font-size: 110%;">**Discussion Questions:** <span style="color: #ff0044; font-family: Tahoma,Geneva,sans-serif; font-size: 110%;">1. What is the name given to a point on a vibrating string at which the displacement is always zero? Node. <span style="color: #ff0044; font-family: Tahoma,Geneva,sans-serif; font-size: 110%;">2. What is the name given to a point at which the displacement is always a maximum? Anti-node <span style="color: #ff0044; font-family: Tahoma,Geneva,sans-serif; font-size: 110%;">3. How is the length of the string related to the wavelength for standing waves? L= nλ/2 <span style="color: #ff0044; font-family: Tahoma,Geneva,sans-serif; font-size: 110%;">4. What is the longest possible wavelength for a standing wave in terms of the string length? 2 x L or two times the string length <span style="color: #ff0044; font-family: Tahoma,Geneva,sans-serif; font-size: 110%;">5. Use your graph to find the frequency for n = 20. (Try it. Does it work?) <span style="color: #ff0044; font-family: Tahoma,Geneva,sans-serif; font-size: 110%;">6. What is the relationship between the speed of the wave and the harmonic number? Constant. <span style="color: #ff0044; font-family: Tahoma,Geneva,sans-serif; font-size: 110%;">7. What is the relationship between the speed of the wave and the frequency? There is a direct relationship. <span style="color: #ff0044; font-family: Tahoma,Geneva,sans-serif; font-size: 110%;">8. What is the relationship between the wavelength and the harmonic number? There is an inverse square relationship. <span style="color: #ff0044; font-family: Tahoma,Geneva,sans-serif; font-size: 110%;">9. What is the relationship between the wavelength and the frequency? There is an inverse relationship

<span style="color: #ff0044; font-family: Tahoma,Geneva,sans-serif; font-size: 110%;">Notes:


 * 1) <span style="color: #ff0044; font-family: Tahoma,Geneva,sans-serif; font-size: 110%;">Standing waves are made by the interference of two waves traveling in opposite directions with the same frequency and amplitude
 * 2) <span style="color: #ff0044; font-family: Tahoma,Geneva,sans-serif; font-size: 110%;">Positions on a standing wave:
 * <span style="color: #ff0044; font-family: Tahoma,Geneva,sans-serif; font-size: 110%;"> node : a point where the amplitude is zero or a minimum (always form at fixed ends )
 * <span style="color: #ff0044; font-family: Tahoma,Geneva,sans-serif; font-size: 110%;"> antinode : a point where the amplitude is a maximum (always form at free ends )
 * 1) <span style="color: #ff0044; font-family: Tahoma,Geneva,sans-serif; font-size: 110%;">Resonance is the increase in amplitude of a periodic system that occurs when the frequency applied equals the natural frequency of the system
 * 2) <span style="color: #ff0044; font-family: Tahoma,Geneva,sans-serif; font-size: 110%;">Standing waves form during resonance but not vice versa
 * 3) <span style="color: #ff0044; font-family: Tahoma,Geneva,sans-serif; font-size: 110%;">A wave moving in a medium of finite length, can interfere with its own reflection to produce a standing wave if it has the same frequency as one of the natural frequencies of the medium
 * 4) <span style="color: #ff0044; font-family: Tahoma,Geneva,sans-serif; font-size: 110%;"> Harmonics are the set of standing waves & are infinite
 * 5) <span style="color: #ff0044; font-family: Tahoma,Geneva,sans-serif; font-size: 110%;">Groups of harmonics:
 * <span style="color: #ff0044; font-family: Tahoma,Geneva,sans-serif; font-size: 110%;"> fundamental : harmonic with the lowest frequency and longest wavelength
 * <span style="color: #ff0044; font-family: Tahoma,Geneva,sans-serif; font-size: 110%;"> overtones : harmonics other than the fundamental