This is only my notes about the course, here can be parts from official notes which are not owned by me or written. source: https://openstax.org/books/college-physics/pages/1-introduction-to-science-and-the-realm-of-physics-physical-quantities-and-units
waves: part 16.9 https://openstax.org/books/college-physics/pages/16-9-waves?query=waves&target=%7B%22index%22%3A0%2C%22type%22%3A%22search%22%7D#import-auto-id1023357
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$T$ The time for one complete up and down motion is the wave’s period. => The wave’s frequency is$f=1/T$ . - The water wave in the figure also has a length associated with it, called its wavelength
$\lambda$ , the distance between adjacent identical parts of a wave, the distance parallel to the direction of propagation. - wave velocity
$v_W$ , the speed of propagation:$v_W = \frac{\lambda}{T} = f\lambda$ - this is the speed of a surface wave;
- for sound,
$v_W$ is the speed of sound - for visible light,
$v_W$ is the speed of light
Many people think that water waves push water from one direction to another. In fact, the particles of water tend to stay in one location, save for moving up and down due to the energy in the wave. The energy moves forward through the water, but the water stays in one place. If you feel yourself pushed in an ocean, what you feel is the energy of the wave, not a rush of water.
Waves may be transverse, longitudinal, or a combination of the two. (Water waves are actually a combination of transverse and longitudinal.)- transverse:
- The waves on the strings of musical instruments
- electromagnetic waves longitudinal:
- Sound waves in air
- Sound waves in water
| In this example of a transverse wave, the wave propagates horizontally, and the disturbance in the cord is in the vertical direction. | In this example of a longitudinal wave, the wave propagates horizontally, and the disturbance in the cord is also in the horizontal direction. |
Most waves appear complex because they result from several simple waves adding together.
superposition: When two or more waves arrive at the same point, they superimpose themselves on one another. More specifically, the disturbances of waves are superimposed when they come together. Each disturbance corresponds to a force, and forces add. If the disturbances are along the same line, then the resulting wave is a simple addition of the disturbances of the individual waves—that is, their amplitudes add. When two or more waves arrive at the same point, they superimpose themselves on one another. More specifically, the disturbances of waves are superimposed when they come together.
| Pure constructive interference of two identical waves produces one with twice the amplitude, but the same wavelength. | Pure destructive interference of two identical waves produces zero amplitude, or complete cancellation. |
An example of sounds that vary over time from constructive to destructive is found in the combined whine of airplane jets heard by a stationary passenger. The combined sound can fluctuate up and down in volume as the sound from the two engines varies in time from constructive to destructive. These examples are of waves that are similar.
Unmoving waves can be seen on the surface of a glass of milk in a refrigerator, for example. Vibrations from the refrigerator motor create waves on the milk that oscillate up and down but do not seem to move across the surface. These waves are formed by the superposition of two or more moving waves.
The waves move through each other with their disturbances adding as they go by. If the two waves have the same amplitude and wavelength, then they alternate between constructive and destructive interference. The resultant looks like a wave standing in place and, thus, is called a standing wave. Waves on the glass of milk are one example of standing waves. There are other standing waves, such as on guitar strings and in organ pipes. With the glass of milk, the two waves that produce standing waves may come from reflections from the side of the glass.
A closer look at earthquakes provides evidence for conditions appropriate for resonance, standing waves, and constructive and destructive interference. A building may be vibrated for several seconds with a driving frequency matching that of the natural frequency of vibration of the building—producing a resonance resulting in one building collapsing while neighboring buildings do not. Often buildings of a certain height are devastated while other taller buildings remain intact. The building height matches the condition for setting up a standing wave for that particular height. As the earthquake waves travel along the surface of Earth and reflect off denser rocks, constructive interference occurs at certain points.
- Nodes: points where the string does not move; more generally, nodes are where the wave disturbance is zero in a standing wave.
- Antinode: the location of maximum amplitude in standing waves.
The wavelength λ is determined by the distance between the points where the string is fixed in place. The lowest frequency, called the fundamental frequency, is thus for the longest wavelength, which is seen to be
The fundamental frequency is
overtones or harmonics:
The first harmonic:
$\lambda_2 = L \Rightarrow f_2 = \frac{v_W}{\lambda_2} = \frac{v_W}{2L} = 2f_1$ similary$f_3 = 3f_1$ .All of these frequencies can be changed by adjusting the tension in the string. The greater the tension, the greater
$v_W$ .