Waves Paz



Definitions and Formulas

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The sound is a wave. If a string of a violin or a harp vibrates back and forth, it is compressing and expanding the surrounding air, thus producing a sound. The high-pressure regions are called compressions and the low-pressure regions are called rarefactions. These compressions and rarefactions travel through the air in the form of longitudinal waves, which have the same frequency as the sound source. In longitudinal waves, the molecules in the air move parallel to the motion of the wave. They compress in the same direction as they travel. These waves travel from sound sources and transmit the energy of the voice or vibrating string. Note that the air does not move when the sound travels through it — only the vibrations move. Louder sound means more powerful compressions and rarefactions.

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The number of these vibrations per second is called the frequency, which is measured in hertz. The period is the duration of time in one vibration or cycle and is measured in seconds. It is the reciprocal of the frequency. The wavelength is the distance over which the wave’s shape repeats. It is inversely proportional to the frequency of the wave if we assume that the wave is moving at a fixed speed.

At 20 °C or 68 °F, the sound is traveling in dry air at about 343 meters per second or 1125 feet per second or a 1 kilometer per approximately 3 seconds. It travels faster in liquids and even faster in solids. For example, the sound travels in water 4.3 times faster than in air, in glass 13 times faster than in air and in diamond it travels 35 times faster than in air.

Though sound waves and water waves travel much more slowly than electromagnetic waves, the equation that describes these wave motions is the same for all three types of wave:

or

where

f is the frequency of wave,

v is the speed of wave, and

λ is the wavelength of wave.

Longitudinal and Transverse Waves

The sound is transmitted through various media as different kinds of waves. It is transmitted through gases and liquids as longitudinal waves. When sound is propagated through solids, it can be transmitted as both longitudinal waves and transverse waves.

To understand both kinds of waves, it is convenient to use a stretched Slinky spring, which will represent the medium (liquid or gas). When you compress and then release the Slinky spring’s coils at one end, the squeezed coils move forward thus transferring energy from one end of the spring to another. When a sound is propagating through liquid or gas, it travels away from the source as periodic compressions of the gas or liquid moving from the source.

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We can compare the spring coils to air or water molecules bumping against each other. Because the direction of these compressions is parallel to the direction of wave propagation, this wave is called longitudinal.

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If you move one end of the Slinky spring representing the medium perpendicular to it, a transverse wave is created. It is called transverse because the motion of the spring coils is perpendicular to the wave motion along the Slinky. The energy is transferred along the spring while its coils move in the direction, which is perpendicular to the direction of energy transfer.

Note that the spring represents the medium in which a wave is propagating and this medium does not travel with the sound wave. It only vibrates. We can easily observe this in a solid and the same is true for any liquid or gas. That is, the molecules of liquid or gas transport the vibration while the average position of the molecules does not change over time for any kind of waves.

Examples

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Let us play several sounds on a keyboard and show you their frequency and wavelength. Assuming that sound travels at the speed of 340 meters per second, we can calculate the wavelength of notes:

Scientific name of the noteFrequency, HzPeriod, msWavelength, cm
A32204.55156
A44402.2778
A58801.1439
A617600.5719.5