sound waves / features of sound waves / superposition
Sound is a disturbance of mechanical energy that propagates through matter as a longitudinal wave. Sound is characterized by the properties of sound waves, which are frequency, wavelength, period, amplitude, and speed. Humans perceive sound by the sense of hearing. By sound, we commonly mean the vibrations that travel through air and can be heard by humans. However, scientists and engineers use a wider definition of sound that includes low and high frequency vibrations in air that cannot be heard by humans, and vibrations that travel through all forms of matter, gases, liquids and solids.
The matter that supports the sound is called the medium. Sound propagates as waves of alternating pressure, causing local regions of compression and rarefaction. Particles in the medium are displaced by the wave and oscillate. The scientific study of sound is called acoustics.
Noise is often used to refer to an unwanted sound. In science and engineering, noise is an undesirable component that obscures a wanted signal.
The speed at which sound travels depends on the medium through which the waves are passing, and is often quoted as a fundamental property of the material. In general, the speed of sound is proportional to the square root of the ratio of the elastic modulus (stiffness) of the medium and its density. Those physical properties and the speed of sound change with ambient conditions. For example, the speed of sound in air and other gases depends on temperature. In air, the speed of sound is approximately 344 ms-1, in water 1500 ms-1 and in a bar of steel 5000 ms-1.
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Features of Sound Waves
The back-and-forth vibration of an object creates the compression waves of sound. The motions of a loudspeaker cone, drumhead and guitar string are good examples of vibration that cause compression waves.
This is different than the up and down or transverse motion of a water wave.
Transverse Wave (water wave)
Compression Wave (sound) above and below
The illustration above shows a comparison of a transverse wave such as a water wave and the compression wave sound wave. Because it is difficult to draw the particles in a sound wave, for convenience we often represent sound waves as transverse wave. The transverse wave representation would show you the diplacement of each particle in the wave from its rest position with repect to the distance along the wave. Compressions in sound waves (where particles are bunched up at high pressures) represent the peaks in the transverse wave. Rarefactions (where the particles are spread out at low pressures represent the troughs.
The pitch of a sound wave is proportional to its frequency. High pitched sounds have high frequencies and low pitched sounds have low frequencies.
The volume of a sound is related to the amplitude of the sound wave. Loud sounds are produced from waves with large amplitudes.
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We shall now look at what happens when two waves interact. If two jets of water interact, they will mix and there are collisions between droplets causing a change in speed and direction. This does not happen with waves. If two waves interact, a new wave is temporarily formed, after which the two waves carry on with exactly the same properties as before, as if nothing had happened. The waves are superposed. Superposition can only be applied to waves of the same kind. Light and sound waves cannot superpose but light and X-rays can because they are both electromagnetic.
Let us look at two waves of different wavelengths crossing and superposing. The resultant wave can be worked out by the vector sum of the two waves.
The principle of superposition of waves can be used to explain the presence of beats in sound, interference effects and standing waves.
We can use the superposition of waves to explain interference. When two waves meet, the amplitude of the resultant wave will not only depend on the amplitude of the two waves, but also their phase relationship. Let us look at two waves of equal amplitude superposing.
In the above case the waves are in phase. The resultant wave is double the amplitude of the original waves. This is called constructive interference or reinforcement.
If the waves are 180° (π radians) out of phase (above), the waves cancel each other out. This is called destructive interference or cancellation. If the phases are different to these values, the resultant amplitude are between these two extremes.
Consider the two waves below that are 180° out of phase, but have different amplitudes.
What would the resultant wave look like?
When light waves pass through a narrow slit, they bend or diffract.
The diffraction of the waves cause the initial waves to become out of phase with each other. This in turn causes interference. Regions of destructive interference show up as dark areas while regions of constructive interference show up as bright areas. This was first demonstrated by Young in the early 1800s it what has become the famous ‘Double Slit Experiment’.
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download activity 8.2.2 - graphing longitudinal waves
download activity 8.2.5 - superposition
download answers to activity 8.2.5 - superposition