Standing Waves Flashcards
Describe how a standing wave is created with a driving oscillator at different frequencies.
Progressive waves are transmitted and reflected at boundaries. With a stretched string, waves generated are reflected back and forth. At most frequencies a jumbled mess is made, but when an exact number of waves are produced when one wave moves to to the end and back, the original and reflected waves reinforce each other at resonant frequency.
For standing waves to be produced, what terms must stand?
The waves must be coherent, being equal amplitude and frequency, and travelling opposite.
What calculates the resonant frequency?
An oscilloscope.
Nodes occur at …. and antinodes occur at….
Min amplitude, max amplitude.
How can frequency be found with a cathode ray oscilloscope, (CRO)?
The CRO measures voltage, displaying waves from an oscillator as a function of voltage over time.
The screen is split into divisions… vertical axis: voltage,, controlled by gain dial for divisions, horizontal axis: time, controlled by timebase dial.
T is found by multiplying the number of squares per wavelength by the timebase value each square. Frequency = 1 / time period. (Hz)
For length L, what is the fundamental frequency/first harmonic wavelength and how many loops are there?
1/2 a wavelength, 1 loop.
For length L, what is the wavelength for the second harmonic/first overtone, how about for the third harmonic/second overtone?
2nd = 1 wavelength, 2 loops. 3rd = 1.5 wavelengths, 3 loops.
For length L is closed end instruments, what’s the maximum wavelength? Nodes occur at which end?
1/4 of a wavelength for length, with nodes forming at the closed end. (lowest resonant frequency)
For length L open end air column instruments, what’s the maximum wavelength? Antinodes occur at which end?
1/2 of a wavelength, with antinodes at the open ends.
lowest resonant frequency
How are standing waves created in string instruments?
Progressive waves are created when the finger plucks the instrument, creating vibrations at a point of contact. The waves, of equal frequency and amplitude and wavelength, travel opposite, are reflected, and superpose to produce a transverse standing wave.
How can the speed of sound be found using a resonance tube?
Create a resonance tube with a hollow tube placed in a measuring cylinder of water.
Choose a tuning fork and note frequency.
Tap it and hold it above the hollow tube. Sound waves are reflected at the air/water surface.
Move the tube up and down to find the shortest distance from the top of the tube and water level that sound resonates at to produce a maximum amplitude.
Measure distance. L= wavelength/4. Find the wavelength and then multiply by frequency to find c. Repeat at different frequencies. The next harmonic can be found moving the tuning fork higher, until L = 3*wavelength/4.
