Conceptual Physics

(Sean Pound) #1

What are the frequency f and the


periodT of the wave?


f = 3.0 cycles/2.0 s


f = 1.5 Hz


T = 1/ f = 1 /1.5 cycles


T = 0.67 s


15.7 - Wave speed


How fast a wave moves through a medium is called its wave speed. Different types of
waves have vastly different speeds, from 300,000,000 m/s for light to 343 m/s for sound
in air to less than 1 m/s for a typical ocean wave. The wave in the string to the right
might be moving at, say, 15 m/s.


The speed of a mechanical wave depends solely on the properties of the medium
through which it travels. For example, the speed of a wave in a string depends on the
linear mass density and tension of the string. This relationship is explored in another
section.


For periodic waves there is an algebraic relationship between wave speed, wavelength
and period. This relationship is shown in Equation 1.


This relationship can be derived by considering some of the essential properties of a
wave. Wavelength is the distance between two adjacent wave peaks. The period is the
time that elapses when the wave travels a distance of one wavelength. If you divide
wavelength by period, you are dividing displacement by elapsed time. This is the
definition of speed.


Because frequency is the reciprocal of period, the speed of a wave also equals the
wavelength times its frequency. Both of these formulations are shown to the right.


Since the speed of a wave is dictated by the physical characteristics of its medium, its
speed must be constant in that medium. In the example of the string mentioned above,
the constant speed is determined by the linear density and tension of the string.


Because the speed of a wave in a medium is constant, the product of its wavelength
and frequency is a constant. This means that for a wave in a given medium the
wavelength is inversely proportional to the frequency. Increase the frequency of the
wave and the wavelength decreases. Decrease the frequency and the wavelength
increases.


Consider sound waves. Different sounds can have different frequencies. If this were not
the case, there would be no music. For example, consider the first four notes of
Beethoven’s Fifth Symphony (the famous “dut dut dut daaah”). As played by the violins,
the first three identical notes are the G above middle C and have a frequency of
784.3 Hz and a wavelength of 0.434 m, while the fourth note (E flat) has a frequency of
622.4 Hz and wavelength of 0.547 m.


Wave speed


How fast a wave travels


v = wave speed


Ȝ = wavelength


T = period


f = frequency


Copyright 2007 Kinetic Books Co. Chapter 15^299

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