For this unit we studied mechanical waves. Unlike electromagnetic waves, mechanical waves need a medium to travel through.
There are two types of mechanical waves:
Transverse waves:
Transverse waves:
Wtransverse waves oscillate perpendicular to the direction they travel. You can model transverse waves with a sinusoidal wave, and you can use that model to evaluate the properties of the wave:
Amplitude: the amplitude is the maximum displacement from the midpoint (equilibrium) to a crest or trough.
Period: the time it takes to complete one cycle
Frequency: the number of waves that occur for a given period of time (meters/second)
Period and frequency are perfectly inversely related, so you can use one to find the other
wavespeed: represented by the letter "v," wavespeed is the quotient of wavelength and the period, otherwise represented by the product of the frequency and the wavelength.
Wavelength is the distance between two equal points on a wave: easiest points to use to determine equilibrium are the midpoint, the crests, or the troughs
Note** wavespeed is neither determinate upon the frequency nor the wavelength. Wavespeed is determined by the medium through which it travels (equations to determine it are below)
Other important equations for this unit that are not on the equation sheet are:
wavespeed = square_root(Tension/linear mass density)
Linear mass density = m/L
Amplitude: the amplitude is the maximum displacement from the midpoint (equilibrium) to a crest or trough.
Period: the time it takes to complete one cycle
Frequency: the number of waves that occur for a given period of time (meters/second)
Period and frequency are perfectly inversely related, so you can use one to find the other
wavespeed: represented by the letter "v," wavespeed is the quotient of wavelength and the period, otherwise represented by the product of the frequency and the wavelength.
Wavelength is the distance between two equal points on a wave: easiest points to use to determine equilibrium are the midpoint, the crests, or the troughs
Note** wavespeed is neither determinate upon the frequency nor the wavelength. Wavespeed is determined by the medium through which it travels (equations to determine it are below)
Other important equations for this unit that are not on the equation sheet are:
wavespeed = square_root(Tension/linear mass density)
Linear mass density = m/L
Harmonics
The lowest possible frequency of a complex wave is referred to as the fundamental frequency. Higher frequencies are given integer values— 2nd harmonic, 3rd harmonic, etc:
The picture to the right shows all of the different harmonics, including the first (fundamental) harmonic. You can determine the harmonic by counting its number of antinodes (position of max displacement), and on a closed-closed system, that will be your harmonic. On a closed system, counting the number of nodes (position of minimum displacement) will give you the harmonic.
The picture on the left is how you an algebraically use the harmonic to find the wavelength— this is useful when trying to determine either the frequency or the wavespeed, if you have one known.
Wavelength (λ)= (2/[harmonic integer]) * Length of the string (L)
For instance if you were asked to find the wavespeed with a given string that is oscillating at a frequency of 80 hz, and you were given a graph of its transverse pattern, which shows the graph oscillating at the third harmonic, and the length of the String is 50 centimeters, you can find the wavelength (λ) by using harmonic properties: λ = 2/3 * 0.5 λ = 0.33 m, then using the equation for wavespeed you can get v = 80 * 0.33 v = 26.66 m/s
The picture on the left is how you an algebraically use the harmonic to find the wavelength— this is useful when trying to determine either the frequency or the wavespeed, if you have one known.
Wavelength (λ)= (2/[harmonic integer]) * Length of the string (L)
For instance if you were asked to find the wavespeed with a given string that is oscillating at a frequency of 80 hz, and you were given a graph of its transverse pattern, which shows the graph oscillating at the third harmonic, and the length of the String is 50 centimeters, you can find the wavelength (λ) by using harmonic properties: λ = 2/3 * 0.5 λ = 0.33 m, then using the equation for wavespeed you can get v = 80 * 0.33 v = 26.66 m/s
Superposition of waves
When two waves occupy the same space they cause interference. They add or subtract their amplitudes, depending on the phase that they are in. There are 2 types of interference: constructive and destructive
Constructive interference is when the sum of their amplitudes is greater than any of their individual amplitudes
Destructive interference is when the sum of their amplitudes is less than any of their individual amplitudes
Constructive interference is when the sum of their amplitudes is greater than any of their individual amplitudes
Destructive interference is when the sum of their amplitudes is less than any of their individual amplitudes
Beat Frequency
A beat frequency is when 2 superimposed waves of very similar frequency interact. The resultant sound contains beats that you can distinctively hear. To calculate the beat frequency use the equation f_beat = abs_value(f_1 - f_2)
A standing wave is a wave, which oscillates back and forth through a medium with a constant amplitude. It oscillates back and forth because there an object at one end of the wave that makes the wave reflect, and go back.