Representing Sound as Pressure Waves

Longitudinal Wave Characteristics Travelling Through Different Media

Sounds are pressure waves reaching our hearing apparatus by the movement of surrounding air molecules. Studying waves helps us to understand basic transport mechanisms.

All sounds are produced by vibrations. 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.

Waves share some characteristic properties and behaviours (Chapman et al, Heinemann Physics 12, Harcourt Education, 2007). Categorization of waves is according to direction of movement of individual particles of the medium relative to travel direction (see also Fig. 1):

• 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.

Longidutinal Waves

Sound waves are called longitudinal (or compression) waves because particle vibration is in the same direction as the line of travel. Particles do not keep moving forward; that is, sound waves transfer energy without transferring particles, which vibrate back and forth about their equilibrium positions. An applet may be viewed to help visualise 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 (see Fig. 2):

• Wavelength, lamda, 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 = lamda / T. Substituting 1/f for the period, wave speed may be written:

Wave speed: v = f x lamda

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? 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 lamda the subject: lamda = 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.

For a fixed medium, the wave speed equation may written as v = f x lamda = constant. Therefore changing source frequency must have the effect of changing wavelength (and vice versa), so as to keep the speed constant. This means that:

Rule: 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.

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 in more details on this topic or to learn about the diffraction of sound waves.

The copyright of the article Representing Sound as Pressure Waves in Physics is owned by Harry P. Schlanger. Permission to republish Representing Sound as Pressure Waves in print or online must be granted by the author in writing.

Notes

Fig 1. Type of Waves

Fig 2. Wave Properties