Sound Waves Can Travel in Solids Liquids and Gases
CH 12 Notes
12.1 Characteristics of Sound:
Sound waves can travel in solids liquids and gases.
The speed of sound in air is 343m/s, in fresh water 1440m/s, in salt water 1560m/s and in steel approximately 5000m/s
The speed of sound is varies with temperature. The speed of sound at zero degrees Celsius is 331m/s.
To account for changing temperature use the following formula;
Speed of sound in air = 331m/s + (0.6)(OC)
Two aspects of sound are Loudness and pitch.
Loudness is related to the intensity which is the energy per unit time over the unit area. This is better known as Watts/meter squared.
Pitch refers to a qualitative and quantitative property of sound. Qualitatively it refers to how high the sound is for the human listener. Quantitatively it refers to the frequency of the sound in Hertz.
AudibleRange - 20Hz to 20,000Hz
Ultrasonic – frequencies over 20,000Hz. Dogs are capable of hearing 50,000Hz and bats 100,000Hz.
Sonar which makes use of ultrasonic frequencies is only one application; others include ultrasound and medical imaging.
Infrasonic – frequencies less than 20Hz. These types of frequencies are created by earthquakes, thunder, volcanoes, and heavy machinery. These low frequency waves can do damage to the human body as they can create resonant wave action of the body’s organs.
Longitudinal waves – often described in the movement of molecules in the direction of energy can also be described in pressure variation and is easier to measure then molecular displacement. The higher pressure occurs at compression sites and lower pressure occurs at rarefaction sites.
12.2 Intensity of Sound: Decibels
Loudness is a qualitative quantity related to the consciousness of the human being. Intensity refers to a quantitative value of sound that is measured in Watts/m2
There are two ways to measure sound and they are related. They include sound level measured in decibels and Intensity measured in W/m2
These measures of sound “loudness” have a range.
Sound Level – 0dB to 120dB threshold of hearing to threshold of pain.
Intensity – 1 x 10-12 W/m2 to 1 W/m2
To produce a sound that is twice as loud, the sound wave has about ten times the intensity.
Because of this relationship between the subjective sensation of loudness and the physically measureable quantity “intensity,” sound levels are usually specified on a logarithmic scale.
The unit on this scale is a bel or more commonly the decibel dB.
The sound level “β” of any sound is defined in terms of intensity “I”
Where Io is the intensity at the threshold of hearing = 1 x 10-12 W/m2
An increase in intensity by a factor of 100, (102), corresponds to a sound level increase of 20dB. Thus a 50dB sound is 100 times more intense than a 30dB sound.
To calculate the intensity of a sound
To calculate the decibels
It is worth noting that a sound level difference of 3dB corresponds to a double intensity or halving the intensity as seen in Example 12.4 - So if you half the sound there is only a decrease of 3dB for each halving of the sound.
The intensity of a wave is proportional to the square of the wave amplitude. Knowing that, we can relate the amplitude quantitatively to the intensity or decibel level.
See example 12-6
We see from this example, how incredibly sensitive the human ear is: it can detect displacements of air molecules which are actually less than the diameter of atoms.
12.4 Sources of Sound: Vibrating Strings and Air Columns
The source of any sound is a vibrating object.
Standing waves are produced and the source vibrates at its natural resonant frequency.
The vibrating source is in contact with the air and pushes on it to produce sound waves that travel outward.
The frequency of the outgoing waves is the same as the source.
The speed and wavelengths of the outgoing waves can be different.
Note that one octave corresponds to a doubling of frequency. An example is middle C and C above middle C with frequencies of 262Hz and 524Hz correspondingly.
Stringed Instruments
Standing waves can be established on a string.
The pitch is normally determined by the lowest resonant frequency or fundamental frequency. This is where the nodes occur only at the ends and the antinode is at the center.
The string that vibrates up and down at the fundamental frequency corresponds to half a wavelength. Therefore, the wavelength of the fundamental frequency is twice the length of the string.
where v is the velocity of the wave on the string and L is the string length.
The possible frequencies for standing waves on a stretched string are whole number multiples of the fundamental frequency.
where n = 1,2,3,… n=1 refers to the fundamental frequency and n=2,3,… are the overtones. All of the standing waves 1 to etc. are considered harmonics and are named for the “n” value. Example, first harmonic, second harmonic, …
If a capo or finger is used to press the string against the fret, the length of the sting changes and the frequency of the vibrating string changes. Also, different frequencies can be created by using strings that have the same length but different mass. To calculate the frequency requires two formulas
to find the velocity of the wave on the spring then to find the new frequency.
How would this knowledge connect to the manufacturing of strings for instruments?
Because vibrating strings are to thin to compress and expand much air, stringed instruments make use of a mechanical amplifier known as a sounding board or sounding box. When the string vibrates at a particular frequency it creates vibration in the sounding board/box at the same frequency which then acts to amplify the frequency.
Wind Instruments
Instruments such as woodwinds, the brasses, and the pipe organ produce sound from the vibrations of standing waves in a column of air within a tube or pipe. Vibration of the air column occurs by a variety of methods.
The air within the tube vibrates with a variety of frequencies, but only the frequencies that correspond to the standing waves will persist.
There are two types of tubes –
- open at both ends
- open at one end
Remember for tubes, the air is what is vibrating and we can describe the wave in terms of the flow of air – that is in terms of the displacement of air molecules or in terms of the pressure in the air. See the diagram under longitudinal waves above.
For an open tube, look at the displacement of air and pressure variation.
For displacement, there will be an antinode since the air can move freely in and out.
The air in the tube vibrates in the form of a longitudinal standing wave.
Examples of an open tube would be an organ pipe or flute.
An open tube has displacement antinodes at both ends.
There must be at least one displacement node within an open tube for a standing wave to exist.
This also represents the fundamental frequency because the distance between two successive nodes or antinodes is half a wavelength.
For a closed tube, look at the displacement of air and pressure variation.
For displacement, there will be a node at the closed end and the air is not free to move.
The air in the tube vibrates in the form of a longitudinal standing wave.
Examples of an open tube would be an organ pipe.
A closed tube has a displacement node at the closed end and an antinode at the open end.
There must be at least one displacement node within a closed tube for a standing wave to exist.
This also represents the fundamental frequency because the distance between a node and antinode is one-fourth a wavelength.
Only odd harmonics are present because the position of a wave in even harmonics would not have a displacement node at the closed end.