If you agree to the license, it grants you certain privileges that you would not otherwise have, such as the right to copy the book or download the digital version for free from www.lightandmatter.com. 60 Period and frequency of a periodic wave, 60.—Graphs of waves as a function of position, 60.—Wave length, 61.—Wave velocity related to frequency and wavelength, 61.—Sine waves, 63.
Vibrations
Period, Frequency, and Amplitude
The usual physics terminology for motion that repeats itself. and over is periodic motion, and the time required for one repetition is called the period, T. The symbol P is not used because of the possible confusion with momentum.). In the example of the block at the end of the spring, d/1, the amplitude will be measured in distance units such as cm.
Simple Harmonic Motion
If the total force on a vibrating object depends only on the object's position and is related to the object's displacement from equilibrium by an equation of the form F = −kx, then the object's motion shows a sinusoidal graph with period T = 2πp. A gust of wind would now and then cause one of the chandeliers in the cathedral to sway back and forth, and he noticed that regardless of the amplitude of the vibrations, the period of oscillation seemed to be the same.
1.3 ? Proofs
Projected onto a straight line, its motion is the same as the motion of an object acted upon by the force F =−k x. Since this equation is independent of r, T is independent of the amplitude subject to the initial assumption of perfect behavior F = −kx, which in reality will only hold approximately for smallx.
Summary
Problems
6 Archimedes' principle states that an object that is partially or completely immersed in a liquid is subject to a buoyant force equal to the weight of the liquid it displaces. Above: A series of images from the film of the Tacoma Narrows Bridge vibrating on the day it was scheduled to collapse.
Resonance
Energy In Vibrations
We have already seen that the potential energy stored in a spring is equal to (1/2)kx2, so the energy is proportional to the square of the amplitude. The amplitude is 106 times greater, and energy is proportional to the square of the amplitude, so the energy is greater by a factor.
Energy Lost From Vibrations
The amount of work done by friction is proportional to the force and the distance traveled, so the work done in one cycle is proportional to the square of the amplitude. Since both work and energy are proportional to A2, the amount of energy removed by friction in one cycle is a fixed percentage of the amount of energy the system has.
Putting Energy Into Vibrations
As the vibration amplitude increases, the damping force is applied over a longer distance. This means that the amplitude of the steady-state response is largest in proportion to the amount of driving force when the driving force matches the natural frequency of vibration.
2.4 ? Proofs
Energy is proportional to A2, i.e. the inverse of the quantity within the square root in equation 4. We assume that the resonance width is small compared to the resonant frequency, so f and fres can be taken as synonyms. The energy of a vibration is always proportional to the square of the amplitude, assuming the amplitude is small.
4 (a) Let W be the amount of work done by friction in the first cycle of the oscillation, i.e., the amount of energy lost as heat. Over much longer time scales (hours), the thread eventually resets itself to its original equilibrium angle (shown as zero degrees in the graph). The graph reproduced here only shows motion on a much shorter time scale.) Some man-made materials also have this "memory" property, but they usually need to be heated in order to return them to their shapes. original.
Free Waves
Wave Motion
Superposition
There are three main ways in which wave motion differs from the motion of objects made of matter. Experiments to date have shown no deviation from the principle of superposition in the case of light waves. If the two pulses essentially canceled each other out perfectly, then why does the motion pick up again.
The movement of the wave pattern is to the right, but the medium (the spring) moves up and down, not to the right.
The medium is not transported with the wave
The mistaken belief that the medium moves with the wave is often reinforced by incorrect second-hand knowledge of surfing. Anyone who has actually surfed knows that the front of the board pushes the water to the sides, creating a wake - the surfer can even drag his hand through the water, as in figure f. If the water moved with the wave and the surf, this would not happen.
The surfer is carried forward because forward is downhill, not because of any forward flow of the water. If the water was flowing forward, a person floating in water up to their neck would be carried along as fast as a person on a surfboard.
A wave’s velocity depends on the medium
- Waves on a String
- Sound and Light Waves
- Periodic Waves
- The Doppler Effect
As always, the speed of the wave depends on the properties of the medium, in this case the string. The size of a radio antenna is closely related to the wavelength of the waves it is intended to receive. For velocities small compared to the wave speeds, the Doppler shifts of wavelength and frequency are approximately the same.).
Did this mean that Earth (or at least our galaxy) was the center of the universe? No, because Doppler light shifts depend only on the relative motion of the source and observer. For some types of waves, especially water waves, the speed can also depend on the shape of the wave.).
Sound waves consist of (usually very small) increases and decreases in air density.
Bounded Waves
Reflection, Transmission, and Absorption
When we look at a pavement, for example, we actually see the reflection of the sun from the concrete. The leading edge of the pulse is what is reflected first, so it's still ahead when it starts back to the left - it's just that the "ahead" is now in the opposite direction. One possibility is to design the antenna so that the speed of the waves in it is as close as possible to the speed of the waves in the cable; this minimizes the amount of reflection.
Just as crudely, we could forget the wave ideas and consider the middle ear purely as a mass on a spring. Diagnosing such a condition is the purpose of the third hole in the probe, which is used to vary the pressure in the ear canal.
4.2 ? Quantitative Treatment of Reflection
Interference Effects
If you look at the front of a high-quality pair of binoculars, you will notice a greenish-blue coating on the lenses. We will analyze the way the coating works, not because optical coatings are an important part of your education, but because it provides a good example of the general phenomenon of wave interference effects. In Figure 4, two pulses are returning to the left, and a single pulse is traveling to the right.
The amount of delay between them depends entirely on the width of the middle segment of the string. How would it change if you gradually raised the bottom edge of the top slide until the two slides were finally parallel.
Waves Bounded on Both Sides
The lowest frequency standing wave is therefore one where 1/4 of a wavelength fits along the length of the tube, as shown in Figure z/3. Draw a graph of pressure versus position for the first overtone of the air column in a tube that is open at one end and closed at the other. How many times shorter will the wavelength be compared to the wavelength of the lowest frequency standing wave shown in the figure.
Whenever a wave encounters the boundary between two media in which its velocities are different, part of the wave is reflected and part is transmitted. The greater the difference in wave speed between the two media, the greater the fraction of wave energy that is reflected.
Exercises
Exercise 1A: Vibrations
Exercise 2A: Worksheet on Resonance
Photo Credits
Except as specifically noted below or in parentheses in the image title, all illustrations in this book are copyrighted by me and are copyrighted under the same license as the rest of the book. In some cases, the date indicates that the figure is in the public domain, but I do not know the name of the artist or photographer; I would appreciate anyone who could help me with proper credit. When "PSSC Physics" is listed as a credit, it means that it is a number from the first edition of the Physics textbook, published by the Board of Studies in Physical Sciences.
Credits to Millikan and Gale refer to the textbooks Practical Physics (1920) and Elements of Physics (1927). The copyright of the 1927 version was not renewed.) Since it is possible that some of the illustrations in the 1927 version have been copyright renewed and are still under copyright, I only used them when it was clear that they originally came from public sources. domain resources. 75Human Cross-Section: Courtesy of the Visible Human Project, National Library of Medicine, US NIH.
Hints and Solutions
Answers to Self-Checks
White light is a mixture of all the colors of the rainbow, and a certain place on the soap bubble can contain part of the mixture, e.g. red, is strongly reflected, while another part, e.g. blue, almost exclusively transmitted. Three-quarters of a wavelength fits into the tube, so the wavelength is three times shorter than that of the lowest frequency mode where one-quarter of a wave fits. Since the wavelength is smaller by a factor of three, the frequency is three times higher.
Answers to Selected Homework Problems
Index
Useful Data
Metric Prefixes
The Greek Alphabet
Speeds of Light and Sound
Subatomic Particles
Notation and Units
Conversions
Earth, Moon, and Sun
