|
|
Science
>>
Physics
>>
|
Representing Sound as Pressure WavesLongitudinal Wave Characteristics Travelling Through Different Media
Jun 25, 2010 © Harry P. Schlanger
Sounds are pressure waves reaching our hearing apparatus by the movement of surrounding air molecules. Studying waves helps us to understand basic transport mechanisms.
Vibrations produce all sounds. A guitar string vibrates and sets forth air molecules into
vibratory motion and creates pressure waves, which travel outward from its source.
The human hearing
apparatus is designed to decode this information, and discriminate between pitch, or frequency, and how
loud the sound is.
Types of Waves in General
Waves share prominent properties and behaviours and are categorised according to the
direction of movement of individual particles in the medium, relative to travel direction.
We can see this concept depicted in the above graphic:
- A transverse wave in which particles of the medium move perpendicular to the direction of the wave.
- A longitudinal wave in which particles of the medium move parallel to the direction of the wave.
Longitudinal Waves
Sound waves are of the longitudinal type because the air molecules particle vibrations cause
compressions in the same direction as the line of travel. These particles do not keep moving
forward vibrate back and forth about their equilibrium positions. Sound waves transfer energy without
transferring particles.
This phenomenon can be exemplified in an
animation that
demonstrates this energy transfer process.
Representing Sound as Waves
Longitudinal waves are difficult to visualise, therefore a transverse analogy is used to help with
understanding. The following wave properties are defined:
- Wavelength, lambda, is the distance between two points undergoing corresponding movement
- Amplitude is the maximum air pressure and relates to the loudness
- Period, T, is the time taken for one complete wave to pass a given point
- Frequency, f, determines the pitch of the sound. The unit is the Hertz, or Hz
There exists an inverse relationship between the period of a soundwave and its frequency, mathematically given by:
Period: T = 1/f
Speed v is distance divided by time. If a distance of one wavelength is divided by the time taken to travel
one wavelength (i.e. one period T), then v = lambda / T. Substituting 1/f for the period, wave speed may be
written:
Wave speed: v = f x lambda
Sound travels more rapidly through relatively densely packed materials such as liquids and solids compared
to gases such as air (for example, speed is 1500 m/s in water and 3500 m/s in brass, but only 340 m/s in
air).
Worked Examples
What is the period of a 50 Hz sound source? Ans: Period T = 1/f = 1/50 = 0.02 s (or 20 ms).
What is the wavelength of sound with frequency 500 Hz, travelling through air at 340 m/s? Making lambda
the subject: lambda = v / f = 340/500 = 0.68 m.
Frequency and the Medium
Whilst the speed of sound will vary depending on the medium through which it travels, its frequency will
remain constant. Only by changing the source of the vibration will the frequency change.
The wave speed equation may written as v = f x lambda = constant, for a given medium. Therefore changing
source frequency must have the effect of changing wavelength (and vice versa), so as to keep the speed
constant. This means that frequency is inversely proportional to wavelength.
For example in music, bass sounds have low frequencies or long wavelengths in air, and treble sounds have
higher frequencies or shorter wavelengths in air.
In summary, sounds may be thought of as longitudinal pressure waves. It is useful to study waves to help
with our understanding of energy transport from the source to the human receiver. Speed of sound depends
on the medium in which it travels but the sound's frequency depends only on the vibration of the source
itself.
The reader may be interested to learn about a related topic,
Diffraction of Sound Waves.
References:
- Chapman et al, Heinemann Physics 12, Harcourt Education, Australia, 2007.
The copyright of the article Representing Sound as Pressure Waves: Longitudinal Wave Characteristics Travelling Through Different Media is owned by Harry P. Schlanger. Permission to republish in print or online must be granted by the author in writing.
|
|
Custom Search
Other Articles:
Website Construction:
Gum Leaf Designs © 2011
|
