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Sound

Updated: Oct 23, 2019

Since I was a kid I loved observing airplanes flying in the sky. My life can be resumed to airplanes in a way. But jet flights were always my favorites. I am from Brazil so I would watch the now decommissioned Mirages 2000 fly all the time. And the coolest of all I have probably seen only once in real live, when the fighters break the sound barriers. But this also made me quite curious about sound waves. How do sound waves behave? What is the speed of sound? What is doppler effect?

Sound waves are longitudinal waves, so they can of course only travel through matter, unlike transverse waves. They are form by alternatively compressing and expanding one end. Compressions are those areas where the coils are momentarily close together. Expansions are regions where the coils are momentary far apart. The velocity of a longitudinal wave then is the square root of the Bulk modulus of the material (how resistant it is to compressions) in which the wave is travelling divided by its density, described in the formula:

There are two main things that one may notice about sound, it has a loudness and pitch. They are measured by some physical quantities. Loudness is related to the energy in the sound wave and pitch is related to the frequency of the wave. So the more energetic the wave is, the louder it will be and the higher the frequency, higher the pitch. The human ear recognizes frequencies from about 20Hz to 20,000Hz. This is called the audible range, but it of course varies from person to person and age. Frequencies higher or lower then that do reach the ears, but it is not recognized. Frequencies above 20,000Hz are called ultrasonic and frequencies below 20Hz are called infrasonic.

Intensity of sound is related to its loudness. It is defined as the energy transported by a wave per unit time across unit area and it its proportional to the square of the wave amplitude. And the unity is Wm⁻². The human ear can hear from 10⁻¹²Wm⁻² to 1Wm⁻².

But intensity is normally measured in a logarithmic scale, which unit is Bel efter the creator of the telephone, Alexander Graham Bell, but decibels are more often used (110bel) . So the Intensity level , in decibels, is defined as the equation:

The red dots in the picture represent constructive interference, while the blue dots represent destructive interference. Some earphones and headphones nowadays uses this to “block” the outside sound enable the user to have a better experience.

The Doppler effect

The doppler effect is what occurs when a hushing police car or firetruck passes you. It’s noticeable that the pitch changes as it gets closer and further away from you. This phenomena actually occur in every type of wave, including light, but sound is more noticeable to us.

References:

(1) https://en.wikipedia.org/wiki/Bulk_modulus

(2) Giancoli, C. Douglas. Physics principles with application. 5th edition. New Jersey , Prentice Hall, 1998.