Exploring Sound Waves and Their Functions

Sound. When a drum is struck, the drumhead vibrates, sending vibrations through the air in the form of sound waves. These waves, when reaching the ear, create the sensation of sound.

Sound is defined as a mechanical disturbance that travels through an elastic medium — a material that returns to its original state after being deformed. The medium doesn't have to be air. Metal, wood, stone, glass, water, and other substances conduct sound — in fact, many of them conduct sound better than air.

Fundamentals of Sound

Sound can originate from numerous sources. Common examples include the vibration of a person’s vocal cords, vibrating strings (piano, violin), a vibrating air column (trumpet, flute), and vibrating solids (a door when knocked). The list is endless, as any disturbance to an elastic medium produces sound.

Sound is characterized by two main aspects: pitch and loudness. The pitch ranges from the deep rumble of thunder to the sharp buzz of a mosquito, while loudness varies in intensity. Both pitch and loudness are subjective, influenced by the listener's hearing abilities. On the other hand, measurable sound qualities like frequency and intensity are objective and correlate with pitch and loudness. To understand these, it's essential to examine sound waves and their properties.

The speed of sound varies depending on the medium through which it travels.

Sound Waves

Air, like all matter, is made up of molecules. Even in a tiny section of air, there are countless molecules in rapid motion. These molecules constantly collide with one another and with any objects that come into contact with the air, moving in unpredictable patterns at high speeds.

When an object vibrates, it generates sound waves in the air. For instance, when a drumhead is struck by a mallet, it vibrates, creating sound waves. The vibration causes the drumhead to move alternately inward and outward, pushing against the air. As the air particles strike the drumhead during its outward movement, they rebound with increased energy and speed due to the force exerted by the vibrating drumhead.

As the molecules move faster, they push into the surrounding air. For a brief moment, the area next to the vibrating drumhead experiences a higher concentration of molecules, creating a compressed region. These faster-moving molecules collide with the surrounding air molecules, transferring their energy. This compressed region continues to move outward as the energy from the drumhead's vibrations spreads through the air molecules.

When the drumhead moves inward, the air molecules that strike it rebound with less energy and speed than usual. This causes a momentary reduction in the number of molecules near the drumhead, creating a region of rarefaction. As the molecules in this area collide with slower-moving molecules, they rebound with less speed, and this region of rarefaction also propagates outward.

The wave nature of sound becomes evident when a graph is drawn showing the changes in air molecule concentration as compression and rarefaction pulses pass through a specific point. A sine wave would represent the graph for a pure tone, such as that from a vibrating tuning fork. The graph begins at an arbitrary point where the concentration is normal, and the compression pulse arrives. The distance between the points on the curve from the horizontal axis indicates the deviation in concentration from the normal.

Each compression followed by a rarefaction constitutes one complete cycle. This cycle can also be measured from any point on the curve to its corresponding point. The frequency of a sound is expressed in cycles per second, or hertz (Hz). The amplitude represents the maximum variation in the concentration of air molecules from the normal state.

The wavelength of a sound represents the distance the disturbance travels in one complete cycle. It is connected to the sound's speed and frequency by the equation speed/frequency = wavelength. This implies that sounds with higher frequencies have shorter wavelengths, while those with lower frequencies have longer wavelengths. The human ear is capable of detecting sounds that range from 20 Hz to 20,000 Hz. At room temperature in still air, sounds at these frequencies have wavelengths of 75 feet (23 meters) and 0.68 inch (1.7 cm) respectively.

Intensity refers to the amount of energy transmitted by a sound disturbance, and it is proportional to the square of the wave's amplitude. Intensity is measured in watts per square centimeter or decibels (dB). The decibel scale works as follows: An intensity of 10^-16 watts per square centimeter corresponds to 0 dB. Every tenfold increase in watts per square centimeter results in a 10 dB increase. For example, 10^-15 watts per square centimeter equals 10 dB, and 10^-4 watts per square centimeter is equivalent to 120 dB.

The intensity of sound diminishes quickly as the distance from its source increases. For a point source emitting sound energy evenly in all directions, the intensity decreases in proportion to the square of the distance from the source. For instance, at two feet from the source, the intensity is one-fourth of what it is at one foot, and at three feet, it is only one-ninth of the intensity at one foot.

Pitch

Pitch is determined by frequency. Generally, when frequency increases, the pitch also seems to rise. However, the ability to differentiate between two sounds with frequencies that are close to each other diminishes at the extreme ends of the human hearing range. Additionally, some individuals can distinguish between two nearly identical frequencies better than others. Some trained musicians can detect differences as small as 1 or 2 Hz.

The perception of pitch is influenced by the intensity of the sound, due to the functioning of the hearing mechanism. For example, when a 440 Hz tuning fork (the pitch of A above middle C on the piano) is moved closer to the ear, it is heard as having a slightly lower pitch, almost as if the fork were vibrating at a slower rate.

When a sound source is moving at a high speed, a stationary listener will perceive a higher pitch as the source approaches and a lower pitch as it moves away. This phenomenon, known as the Doppler effect, occurs because of the wave-like behavior of sound.

Loudness

Generally, an increase in intensity leads to a perception of greater loudness, but the relationship is not proportional. A sound at 50 dB is ten times more intense than a sound at 40 dB, yet it is only perceived as twice as loud. The loudness increases by a factor of two with every 10 dB rise in intensity.

Loudness is also influenced by frequency because the human ear is more sensitive to some frequencies than to others. The threshold of hearing — the quietest sound intensity that can be perceived by most people — is around 0 dB in the 2,000 to 5,000 Hz frequency range. For frequencies outside this range, a higher intensity is needed to hear the sound. For instance, a 100 Hz sound is barely audible at 30 dB, and a 10,000 Hz sound is barely audible at 20 dB. At intensities of 120 to 140 dB, most individuals experience physical discomfort or even pain, a level known as the threshold of pain.

Speed of Sound

The speed of sound is influenced by the elasticity and density of the medium it travels through. In general, sound moves faster in liquids than in gases, and faster in solids than in liquids. The speed of sound is determined by the relationship between elasticity and density, where a higher elasticity and lower density lead to faster sound transmission.

This relationship between elasticity and density can be seen in the comparison of sound's speed in different materials like air, hydrogen, and iron. Hydrogen has a similar elasticity to air but a lower density, so sound travels much faster in hydrogen (about four times faster). Although air is less dense than iron, iron's much greater elasticity allows sound to travel significantly faster in it (about fourteen times faster).

The speed of sound varies with temperature, especially in gases and liquids, since temperature changes affect the density of the material. For instance, in air, the speed of sound increases as the temperature rises. At 32 °F (0 °C), the speed is 1,087 feet per second (331 m/s), while at 68 °F (20 °C), it reaches 1,127 feet per second (343 m/s).

The terms 'subsonic' and 'supersonic' are used to describe the speed of an object, such as an aircraft, in comparison to the speed of sound in the air around it. Subsonic refers to speeds slower than sound, while supersonic refers to speeds faster than sound. An object traveling at supersonic speeds creates shock waves instead of regular sound waves. These shock waves, when traveling through air, are typically heard as a sonic boom.

Supersonic speeds are often measured using the Mach number, which compares the speed of an object to the speed of sound in the surrounding air. For example, an object moving at Mach 1 is traveling at the speed of sound, while at Mach 2, it is moving at twice that speed.

The Behavior of a Sound Wave

Similar to light and other types of waves, sound waves can be reflected, refracted, diffracted, and they can also interfere with one another.

Reflection

Sound is constantly bouncing off a variety of surfaces. Most of the time, these reflections go unnoticed because sounds that arrive at the human ear less than 1/15 of a second apart are perceived as one continuous sound. However, when the reflected sound is heard as a distinct repeat, it is called an echo.

When sound reflects off a surface, it does so at the same angle at which it hits. This principle allows sound to be focused using curved surfaces, much like curved mirrors focus light. It also explains the phenomenon of whispering galleries, where a word whispered at one point can be clearly heard at a distant point in the room but not in between. An example of this is the National Statuary Hall in the United States Capitol. This reflective property is also utilized in devices like megaphones and when calling through cupped hands.

In concert halls and auditoriums, sound reflection can create serious issues. In poorly designed spaces, the first word spoken may reverberate for several seconds, causing the audience to hear each word echoing together. This issue can also distort music. The problem can often be solved by using sound-absorbing materials like drapes or acoustic tiles to cover reflective surfaces. Clothing also absorbs sound, which is why reverberation is stronger in an empty hall compared to one filled with people. These sound-absorbing materials trap sound waves by allowing them to bounce around inside tiny air-filled spaces until their energy is depleted.

Some animals, notably bats, use sound reflection for echolocation — a method of locating and identifying objects through hearing instead of sight. Bats emit high-frequency sounds beyond human hearing, which reflect off even the smallest objects. This ability allows a bat to track and catch a mosquito in complete darkness. Sonar technology is a human-made version of echolocation.

Refraction

When a wave transitions from one material to another at an angle, it typically changes its speed, causing the wave front to bend. This change in direction, known as refraction, can be demonstrated in a physics lab by using a lens-shaped balloon filled with carbon dioxide to focus sound waves.

Diffraction

When sound waves encounter an obstacle or pass through an opening, the edge of the obstacle or the opening acts as a secondary source of sound. This secondary source emits waves with the same frequency and wavelength as the original, but at a lower intensity. The spreading of these waves from the secondary source is called diffraction. This is why sound can be heard around corners, even though sound waves typically travel in a straight line.

Interference

Interference occurs whenever waves interact. In the case of sound waves, this interaction can be understood by looking at how their compressions and rarefactions align. When the waves are in phase, meaning their compressions and rarefactions match up, they amplify each other, creating constructive interference. When the waves are out of phase, such that one wave’s compression aligns with the other’s rarefaction, they cancel each other out or weaken, resulting in destructive interference. The result is a new wave formed by the interaction of the two.

In auditoriums, destructive interference between the sound produced by the stage and sound reflections from other parts of the hall can create dead spots where both the volume and clarity of the sound are diminished. This issue can be reduced by placing sound-absorbing materials on reflective surfaces. On the other hand, interference can enhance the acoustics of a space when the reflecting surfaces are arranged to increase the sound level in the audience area.

When two waves with frequencies that are almost, but not quite, identical interact, they create a tone whose intensity alternates between loud and soft as the waves continually shift in and out of phase. These fluctuations are known as beats. Piano tuners use this effect to adjust the tone of a string in relation to a standard tuning fork, fine-tuning until the beats vanish.

Sound Quality

Pure tones with a single frequency are produced only by tuning forks and electronic devices called oscillators. Most sounds, however, are a combination of various frequencies and amplitudes. The tones made by musical instruments share a key characteristic: they are periodic, meaning their vibrations repeat in a regular pattern. This can be seen on an oscilloscope trace of a trumpet's sound. In contrast, most non-musical sounds, such as a balloon popping or someone coughing, produce an irregular, jagged pattern on an oscilloscope, indicating a mixture of frequencies and amplitudes.

Both a trumpet's air column and a piano string have a fundamental frequency — the rate at which they vibrate most easily when set in motion. For a vibrating air column, this frequency is mainly determined by the column's length. (The valves on the trumpet alter the effective length of the column.) In the case of a vibrating string, its fundamental frequency is influenced by the string's length, tension, and mass per unit length.

In addition to the fundamental frequency, a vibrating string or air column generates overtones that are whole-number multiples of the fundamental frequency. The distinct sound or timbre of a musical tone comes from the number of overtones produced and their relative intensities. If more overtones are added, they form a complex pattern, like the oscilloscope trace of a trumpet's sound.

The way a vibrating string's fundamental frequency depends on its length, tension, and mass per unit length is explained by three principles:

1. The fundamental frequency of a vibrating string is inversely proportional to its length.

If the length of a vibrating string is halved, its frequency doubles, raising the pitch by one octave, assuming the tension remains constant.

2. The fundamental frequency of a vibrating string is directly related to the square root of its tension.

When the tension in a vibrating string is increased, its frequency rises. If the tension is increased fourfold, the frequency will double, and the pitch will go up by one octave.

3. The fundamental frequency of a vibrating string is inversely proportional to the square root of the mass per unit length of the string.

This means that, for two strings of the same material, length, and tension, the thicker string will have a lower fundamental frequency. If one string's mass per unit length is four times greater than the other, the thicker string will have half the frequency of the thinner string and produce a tone one octave lower.

History of Sound

In the sixth century B.C., the Greek philosopher and mathematician Pythagoras made one of the earliest observations about sound. He discovered the relationship between the length of a vibrating string and the tone it produces — a principle now known as the first law of strings. Pythagoras likely also realized that the sensation of sound is due to vibrations. Soon after his time, it became clear that sound arises from vibrations traveling through the air and reaching the eardrum.

Around 1640, French mathematician Marin Mersenne conducted pioneering experiments to measure the speed of sound in air. Mersenne is also credited with formulating the second and third laws of strings. Later, in 1660, British scientist Robert Boyle proved that sound requires a medium to travel through by showing that a bell's ringing couldn't be heard in a vacuum, where the air had been removed from the jar.

Ernst Chladni, a German physicist, conducted significant studies on sound vibrations in the late 1700s and early 1800s. Around the same time, French mathematician Fourier discovered that complex waves, such as those created by a vibrating string with all its overtones, are made up of a series of simple, periodic waves.

In the late 1800s, Wallace Clement Sabine, a physicist at Harvard University, made a groundbreaking contribution to acoustics. Sabine was tasked with improving the acoustics of the main lecture hall at Harvard's Fogg Art Museum. He became the first to measure reverberation time, which he found to be 5 1/2 seconds. Through experimentation with seat cushions and various sound-absorbing materials, Sabine established the principles for architectural acoustics. He later designed Boston Symphony Hall (opened in 1900), the first building to incorporate scientifically-based acoustics.

During the second half of the 20th century, growing urban noise levels spurred a new wave of studies focused on the physiological and psychological impacts of noise on humans, particularly in cities where noise pollution had become a significant concern.