Sound Production When you pluck a stretched elastic band, it vibrates to and fro, creating compressions and rarefactions that spread out through the air, forming a longitudinal wave. The air particles vibrate at the same frequency as the elastic and their vibration frequency determines the pitch of the sound. The amplitude of the air particles' vibrations determines the loudness of the sound. Recall that sound waves are a type of mechanical wave and so sound energy must have a transmitting medium through which to move. In some space movies, we see a large space craft moving across the screen and hear the rumble of its powerful engines. Is this accurate?

Echoes Bats emit loud, high pitch screams and listen for the echoes. Their brains interpret the echoes to help them avoid obstacles and locate food. Computers on submarines use sonar echoes in a similar way but the bat’s brain is enormously more efficient at the task of understanding echoes. Porpoises can use their echolocation skills to locate and even identify certain species of fish hiding in sand.

Resonance Sound waves striking a body can cause it to vibrate sympathetically if its natural vibration frequency is the same as the sound's frequency. An example is when we feel the vibrations from a nearby loud base speaker. Also, the windows in our house may rattle due to the low pitch sound of a powerful engine in a passing vehicle.

Resonance in Tubes An acoustic musical instrument is basically just an air filled cavity. Its sound is created by resonance. To play a clarinet for example, the musician first blows through the mouthpiece to get the instrument’s resonator vibrating. The resonator is a reed – a small sliver of bamboo – and it can emit just a tiny sound. Its vibrations move into the body of the clarinet and the air there absorbs the small sound and begins to vibrate at the same frequency, i.e., to resonate. So, the tiny sound is magnified. A given size air cavity will magnify one frequency best but the player wants to produce a variety of notes, all heard equally well by the audience. So, the size of the air cavity must be changed each time a new note is to be played. The musician alters the effective size of the air cavity by opening or closing the holes along the clarinet’s body. Resonance is important to the operation of wind and stringed instruments which are "closed tubes", e.g., guitar, or "open tubes", e.g., clarinet.

Laws of Strings Stringed instruments can produce a variety of pitches because their strings are various lengths (l, in cm or m), diameters (d, in cm), tensions (F, in N), and densities (D, in g/cm³). The way these variables work together to affect the pitch of a sound is described by the Laws of Strings.

Note: Humans make sounds when exhaled air passing by our vocal cords causes them to vibrate. We change the pitch of our voice through tiny muscles that adjust the tension on our vocal cords. At puberty, hormones make the vocal cords of males thicker than those of females and so the male voice tends to have a lower range of frequencies.

Harmonics A string vibrating as a whole, i.e., in one segment, creates its lowest tone, the fundamental or first harmonic. The string will have two nodes (points of no vibration) and one antinode (a location of maximum vibration.) If the string vibrates in two segments, it has three nodes, two antinodes and produces a sound called the second harmonic; its pitch is twice as high as its fundamental. A string vibrating in three segments will have five evenly spaced nodes and three antinodes. Its sound is called the third harmonic and has a pitch three times as high as its fundamental. A long string tends to vibrate in a number of these vibration patterns all at the same time, producing a rich sound full of harmonics. Note: A sound with a frequency double that of another sound is an octave above it. The resonance behavior of sound waves in open tubes enables them to magnify frequencies that are 2, 3, 4, 5, etc. times the fundamental. The resonance behavior of sound waves in closed tubes allows them to magnify frequencies that are 3, 5, 7, etc. times the fundamental.

Beats When two different pitches occur together, we hear a new sound with a wavering or quivering quality. The pitch of this new sound, the beat frequency, is just the mathematical difference of the two original pitches. Because our attention is drawn to the beat frequency and not the individual original sounds, composers must anticipate what new sounds are created by groups of instruments or voices. Certain sounds create beat frequencies that are pleasant to us and we say the sound is a consonance. If the sound of the beat frequency is unpleasant, we call it a dissonance. The blended sound of a barbershop quartet is a consonance.

Doppler Shift When a sound source is motionless, its sound waves spread out in evenly spaced circles. But, if the sound source is moving, the waves in front of it become squished and the waves behind it become elongated. People in front of the moving sound source are in the path of the compressed sound waves and hear a higher than normal pitch; people in the path of the elongated sound waves behind the moving sound hear a lower than normal pitch.

The Ear The ear has three major sections: the outer, middle and inner ear.

Outer ear: The pinna is the fleshy outermost part of our ear. It collects sound waves and directs them into the auditory canal. The auditory canal then directs the sound to the middle ear.

Middle Ear: The tympanic membrane (eardrum), the start of the middle ear, vibrates as the sound waves strike it. Attached to the inside of the eardrum are the three ossicles, the tiniest bones in our body. As they vibrate and transfer sound energy to the inner ear, they magnify it 1.5 times. When a sound reaches a certain intensity, two tiny muscles pull the last ossicle back from the inner ear and this reduces the chance of damage there.

Inner ear: The last ossicle transmits its vibrations into the cochlea, a spiral shaped structure filled with liquid and lined with about 22 000 vibration sensitive nerve hairs. The nerve hairs are grouped into thousands of small rows, each one containing hairs sensitive to a certain frequency. Finally, the auditory nerve gathers all the impulses from the nerve hairs and carries them to the brain's auditory center where we "hear."

Hearing Safety The decibel scale, dB, is used to measure sound intensity. If sounds are loud enough, the extreme frequency range of a very sensitive the human ear is from 20 to 20 000 Hz. Frequencies higher or lower than these are inaudible. Sounds with frequencies above 20 000 Hz are called ultrasonic sounds; those with frequencies below 20 Hz are called infrasonic sounds. And, within the audible frequency range, we do not hear all frequencies equally well.

Audiologists have published charts listing the intensity of common sounds to help people judge the safety of certain sound environments. Note: do not confuse the pitch of a sound (Hz) and its loudness (dB.) Loudness is aspect of a sound that causes the greater damage.

If a sound is loud enough, it causes the eardrum to vibrate so far back and forth that pain is felt. Note that pain can be caused by the loud sounds from a rock concert. In addition to hearing loss, exposure to loud sounds can cause another permanent hearing disorder called tintinitis. The symptom is a constant ringing sound. Sleep is possible only by masking the ringing with louder but soothing sounds, e.g., water sounds.

Sound Oddities

Infrasonic Sound: Elephants can make and hear infrasonic sounds. When they are lying in water, we can see energy ripples moving out from their foreheads but we can not hear the sound. They use infrasonic sounds to communicate with other elephants as far away as 500 miles.

Pigeons can hear the infrasonic sounds made by wind rushing through mountain passes thousands of kilometers away. They use these sounds to help them navigate.

Another long distance listener is the whale. They can also hear infrasoninc sounds made thousands of kilometers away. We think they use these low frequency sounds for communication and navigation.

A bizarre use of infrasonic sound was as a weapon of war. A giant coach’s whistle powered by a huge compressor sent out infrasonic sounds that disoriented the enemy. But, after just a few trials, the sound weapon was taken out of use. Because the sound waves diffracted around the weapon, the operators were subjected to the same energy and became too ill to use it.

Upper Audible Range: Television technicians repairing vacuum tube powered picture tubes used to suffer hearing loss at one specific frequency. It was later realized that one of the TV’s transformers (called a fly-by transformer) gave off a constant 15 000 Hz barely audible squeal. After years of exposure, the technician’s cochlear cells sensitive to that frequency were wrecked.

Ultrasonic Sounds: These super high frequency sounds have a number of uses. They can be used to clean jewellery, measure heart performance, reveal the hidden world of unborn babies, zap painful gallstones into much less painful grit and, as “silent” dog whistles to command trained animals, e.g., dogs, goats.

Q. The specifications of expensive speakers often claim they can create sounds outside your hearing range.

     Are these speakers wasting your money on inaudible frequencies?

Sound Math

Sound Motion

Q. a) The 440 Hz squawk from a parrot will travel 50 m in what time if the Tair is 20⁰C?

     b) Find the wavelength of the squawk.

Q. A girl standing on the floor of a valley fires a rifle and hears the echo from the closer wall after 3 s. She

     hears the echo from the other wall 4 s later. If the Tair is 20⁰C, find the valley width.

Resonance in Tubes

Q. At 10⁰C, a tuning fork resonates with a closed 15 cm long, 2.5 cm diameter tube. What is the tuning

     fork’s frequency?

Q. At 25⁰C, a tuning fork resonates with an open 20 cm long, 3.5 cm diameter tube. What is the tuning

     fork’s frequency?

Laws of Strings

f₂ = l₁ * d₁ * √ F₂ * √ D₁

f₁ l₂ * d₂ * √ F₁ * √ D₂

Q. An 80 cm long, 0.3 cm diameter string tightened to 500 N sounds at 440 Hz. At what frequency will it

     sound if the string is shortened to 60 cm and the tension is increased to 600 N? (What is done with

     variables whose values do not change?)

Q. Decreasing a string's length causes its pitch to ___.

     Increasing a string's diameter causes its pitch to ___.

     Loosening a string causes its pitch to ___.

     Increasing a string's density causes its pitch to ___.

Doppler Shift

Q. A train blowing its 440 Hz horn approaches a station at 30 m/s. If the Tair = 30⁰C, what pitches are

     heard by a motionless listener on the station platform as the train:

     a) approaches b) passes c) retreats?

    fl = fs  v + vl 

               v - vs 

Q. A car blowing its 2000 Hz horn moves at 6 m/s west while a listener moves at 0.5 m/s east. If

     the Tair = 15⁰C, what pitches are heard by the listener during the:

     a) approach b) pass c) retreat phases?

    fl = fs  v + vl 

               v - vs 

Beats

Q. A 350 Hz and a 450 Hz tuning fork are sounded simultaneously. What beat frequency is created?

    Δf = ∣f ₂ – f ₁ ∣

Q. When a 500 Hz tuning fork and a tuning fork of unknown frequency are sounded simultaneously, a

     75 Hz beat frequency is created. What could be the two unknown tuning fork frequencies?

    f ₂ = f ₁ + Δf