Chapter Summary

PREVIEW

This is the first of two chapters covering waves. In this chapter you will become acquainted with the concept of waves, in particular a special wave referred to as a periodic wave. You will learn to describe a periodic wave in space by its wavelength and amplitude and in time by its amplitude and period. Combining these descriptions allows us to find the speed of a wave in terms of its frequency and wavelength. The speed of waves on a stretched string will be investigated. A mathematical description of harmonic waves is given. This is very important since any complicated wave can be described as a sum of harmonic waves, as you will learn in a later chapter.

In this chapter you will also study the nature of sound. The wave properties of sound are examined, including the speed of sound in gases, liquids, and solids. You will be introduced to the concepts of sound intensity, loudness, and the decibel scale. Applications of sound are also discussed, such as sonar, ultrasound, and the Doppler effect.

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Important Terms

Wave A traveling disturbance which carries energy. Mechanical waves require a medium. Transverse wave The wave disturbance is in a direction perpendicular to the direction of wave travel. Longitudinal wave The wave disturbance is parallel to the line of wave travel. Periodic wave The wave disturbance is repeated continuously by the source of the disturbance. Amplitude (A) The maximum excursion of a particle of the medium from the particle's undisturbed position. Wavelength (l) The distance along the length of a wave between two equivalent points. Period (T) The time required for a wave to travel one wavelength. Frequency (f) The number of wavelengths per second which pass a given point. Note: f = 1/T. Speed of a wave The product of the wavelength and the frequency of a wave. Condensation A region of slightly increased air pressure produced by a vibrating source. Rarefaction A region of slightly reduced air pressure immediately following a condensation. Frequency of a sound wave The number of cycles per second (each cycle being composed of one condensation and one rarefaction) that pass a given location. Pure tone A sound containing a single frequency. Pitch A subjective quality related to the freque sound in a liquid is:

Equations

The speed of a periodic wave which has a wavelength, l, and a frequency, f, is

v =lf (16.1) 

The speed of a wave traveling on a string under a tension, F, and having a linear density m/L is

 (16.2) 

The displacement of a particle of the medium from its undisturbed position when a harmonic wave is moving along the + x axis is

y = A sin (2pft - 2px/l) (16.3) 
and for motion of the wave toward - x
y = A sin (2pft + 2px/l) (16.4) 

The speed of sound in a gas is:

 (16.5) 

The speed of sound in a liquid is:

 (16.6) 

The speed of sound in a long, thin, solid bar is:

 (16.7) 

The sound intensity is defined as:

 (16.8) 

If a sound is emitted uniformly in all directions, the intensity at a distance r from the source is:

 (16.9) 

The intensity level in decibels is defined as:

 (16.10) 

The Doppler shifted frequency (general case) is:

 (16.15) 



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