Ultrasonics – Sound – Effect of Speed of Sound on Wavelength

The speed at which sound travels through a sound conducting media varies depending on the media.  In general, sound travels faster in liquids than it does in gasses.  Solids are the best conductors of all beating out both liquids and gasses.  The speed at which sound travels through most materials depends on several variables including temperature and, in the case of gasses, pressure and humidity.  The speed of sound also varies with its frequency but that effect is relatively small at most common frequencies.  If there was a large variation, you would hear the tubas in the orchestra sooner or later than the piccolos and, clearly, that isn’t the case.

When we talk about electromagnetic and light waves, we usually relate frequency directly to wavelength.  In the case of these waves, this is appropriate since the speed of travel does not change that much in different transmission media.  Of course, light and electgromagnetic waves can also travel in a vacuum which sound waves can not.  The fact that the speed of sound varies widely depending on the conducting media means that we can not relate wavelength directly too frequency except in cases where the media remains the same.

Wavelength and frequency are related in the following way.

Wavelength = Speed of sound/Frequency

Typical units are –

Wavelength – Feet
Speed of sound – Feet per Second
Frequency – Cycles per second or Hz

Since the speed of sound is different in different media, this means the the wavelength of sound at a given frequency is a variable depending on the speed of sound in the conducting media.  Using the speeds of sound in the table above, for example, the wavelength of a 100 cycle tone in air at 68ºF would be 11.27 feet while the same tone in fresh water at 68ºF would have a wavelength of 48.05 feet (nearly five times as long).  Similarly, a 100 Hz tone in Steel at 68ºF would have a wavelength of 168.5 feet!  The following illustration will help clarify this concept.

It is important to note that even though the wavelength is different in all three materials, the tone remains the same.  As the sound travels faster or slower, the time difference between the leading edge of the wave and the trailing edge of the wave arrive with the

same differential even though the actual wavelength is longer or shorter.

I am making a big point of this because frequency is often related to wavelength as an inverse ratio.  With sound waves, this relationship, unless the media remains the same, can not be assumed.  This will be important as we go on to talk about resonance and how sound waves are transmitted from one sound conducting media to another.

–  FJF  –