V IBRATIONS & W AVES : Activity 18 – Resonance and Standing Waves

GUIDING QUESTION How do we make and control waves? Waves can be reflected from boundaries, and if the conditions are just right a standing wave forms. A standing waves is an extended oscillation where a whole system can move with a single wave pattern We will use a standing wave to explore the connection between the frequency of a wave and its wavelength. Although we are using a vibrating string to see the wave, this applies to all other waves.

SETTING UP THE EXPERIMENT 1. Connect Timer to the sound and waves generator 1. Connect timer and wave generator using telephone cord 2. Connect wave generator and wiggler using black cord 2. Attach fiddle held to the top of the stand as high as it can go 3. Stretch elastic strand about 5 to 10 cm and attach free end to fiddle head 1. Loosen knob 2. Slide string between any two washers 3. GENTLY tighten knob just enough to hold string

SETTING UP THE EXPERIMENT 4. Turn on the Timer using the AC adapter 5. Use button on lower left to set wave generator to waves (wiggler should start to shake the string) 6. Set timer to measure frequency 1. Get a reading of about 10Hz (wiggler oscillating 10 times per second) 7. Adjust frequency of the wiggler with frequency control on wave generator 1. If you watch the string you will find that interesting patterns form at certain frequencies

FINDING THE STANDING WAVES Standing waves only occur at certain special frequencies. Wiggler applies a periodic force to the string. When periodic force matched the natural frequency of the string, a large response develops (resonance) 1. Use frequency control to find at least the first eight harmonics of the string 2. Record frequency and wavelength for each harmonic. Fine-tune frequency to get largest amplitude wave before recording data.

FREQUENCY, HARMONICS AND WAVELENGTH DATA Harmonic #Frequency (Hz) Wavelength (m) Frequency x Wavelength TIP: look for harmonics 2 – 6 before looking for first one. They are easiest to find and data will give you clues to finding the rest!

THINKING ABOUT WHAT YOU OBSERVED #1 1. Give an equation relating frequency ( f) and wavelength (λ) that best describes your observations. 2. If the frequency increases by a factor of two, what happens to the wavelength? 3. Propose a meaning for the number you get by multiplying frequency and wavelength.

FREQUENCY AND ENERGY Waves are useful because they carry energy from one place to another. The energy of a wave can also carry information such as a cell phone voice signal or TV picture. 1. Set up several wave patterns and measure the amplitude for each harmonic. 2. Measure at least 5 different harmonics, including the 6 th or higher.

FREQUENCY VS AMPLITUDE DATA Harmonic #Frequency (Hz) Amplitude (cm)

T HINKING A BOUT W HAT Y OU O BSERVED #2 1. What happens to the amplitude of the waves as their frequency increases? 2. How does the energy of a wave depend on its frequency if the amplitude stays constant? How is your answer supported by your observations of the vibrating string?

BLOG POST #2 1. In 1 or 2 sentences, describe how the frequencies of the different harmonic patterns are related. 2. Why is the word fundamental chosen as another name for the first harmonic? 3. Find the definition of resonance as it applies to physics. What does resonance have to do with pushing on a swing?