Raymond A. Serway and John W. Jewett. “Physics for Scientists and Engineers with modern physics“, 8th edition, Brooks/Cole, Belmont, USA (2010)

Part 2. Oscillations and Mechanical Waves

Most of the waves we studied in previous sections are constrained to move along a one-dimensional medium. For example, a one-dimensional sinusoidal wave is a purely mathematical construct moving along the x axis. The sinusoidal wave in a string is constrained to move along the length of the string. We have also seen waves moving through a two-dimensional medium, such as the ripples on the water surface in the introduction to Part 2 and the waves moving over the surface of the ocean in previous lectures. In this session, we investigate mechanical waves that move through three-dimensional bulk media. For example, seismic waves leaving the focus of an earthquake travel through the three-dimensional interior of the Earth.

We will focus our attention on sound waves, which travel through any material, but are
most commonly experienced as the mechanical waves travelling through air that result in
the human perception of hearing. As sound waves travel through air, elements of air are
disturbed from their equilibrium positions. Accompanying these movements are changes
in density and pressure of the air along the direction of wave motion. If the source of the
sound waves vibrates sinusoidally, the density and pressure variations are also sinusoidal. The mathematical description of sinusoidal sound waves is very similar to that of sinusoidal waves on strings, as discussed in previous session.

Sound waves are divided into three categories that cover different frequency ranges.

(1) Audible waves lie within the range of sensitivity of the human ear. They can be generated in a variety of ways, such as by musical instruments, human voices, or loudspeakers.

(2) Infrasonic waves have frequencies below the audible range. Elephants can use infrasonic waves to communicate with one another, even when separated by many kilometres.

(3) Ultrasonic waves have frequencies above the audible range. You may have used a “silent” whistle to retrieve your dog. Dogs easily hear the ultrasonic sound this whistle emits, although humans cannot detect it at all. Ultrasonic waves are also used in medical imaging.

This session begins with a discussion of the pressure variations in a sound wave, the speed of sound waves, and wave intensity, which is a function of wave amplitude. We then provide an alternative description of the intensity of sound waves that compresses the wide range of intensities to which the ear is sensitive into a smaller range for convenience. The effects of the motion of sources and listeners on the frequency of a sound are also investigated.

Raymond A. Serway and John W. Jewett. “Physics for Scientists and Engineers with modern physics“, 8th edition, Brooks/Cole, Belmont, USA (2010)

Part 2. Oscillations and Mechanical Waves

Many of us experienced waves as children when we dropped a pebble into a pond. At the point the pebble hits the water’s surface, circular waves are created. These waves move outward from the creation point in expanding circles until they reach the shore. If you were to examine carefully the motion of a small object floating on the disturbed water, you would see that the object moves vertically and horizontally about its original position but does not undergo any net displacement away from or toward the point at which the pebble hit the water. The small elements of water in contact with the object, as well as all the other water elements on the pond’s surface, behave in the same way. That is, the water wave moves from the point of origin to the shore, but the water is not carried with it.

The world is full of waves, the two main types being mechanical waves and electromagnetic waves. In the case of mechanical waves, some physical medium is being disturbed; in our pebble example, elements of water are disturbed. Electromagnetic waves do not require a medium to propagate; some examples of electromagnetic waves are visible light, radio waves, television signals, and x-rays. Here, in this part of the course, we study only mechanical waves.

Raymond A. Serway and John W. Jewett. “Physics for Scientists and Engineers with modern physics“, 8th edition, Brooks/Cole, Belmont, USA (2010)

Part 2. Oscillations and Mechanical Waves

We begin this part of the course by studying a special type of motion called periodic motion, the repeating motion of an object in which it continues to return to a given position after a fixed time interval. The repetitive movements of such an object are called oscillations. We will focus our attention on a special case of periodic motion called simple harmonic motion. All periodic motions can be modelled as combinations of simple harmonic motions.

Simple harmonic motion also forms the basis for our understanding of mechanical waves. Sound waves, seismic waves, waves on stretched strings, and water waves are all produced by some source of oscillation. As a sound wave travels through the air, elements of the air oscillate back and forth; as a water wave travels across a pond, elements of the water oscillate up and down and backward and forward. The motion of the elements of the medium bears a strong resemblance to the periodic motion of an oscillating pendulum or an object attached to a spring.

To explain many other phenomena in nature, we must understand the concepts of oscillations and waves. For instance, although skyscrapers and bridges appear to be rigid, they actually oscillate, something the architects and engineers who design and build them must take into account. To understand how radio and television work, we must understand the origin and nature of electromagnetic waves and how they propagate through space. Finally, much of what scientists have learned about atomic structure has come from information carried by waves. Therefore, we must first study oscillations and waves if we are to understand the concepts and theories of atomic physics.

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