With a wave in a string, a complete cycle of motion occurs when a particle in the string
starts at a point (perhaps a peak), moves to a trough, and returns to a peak. With a
sound wave, an analogous cycle passes from compression to rarefaction and then
returns to compression.
To measure the period, you can note how long it takes for an air particle to pass
through a complete cycle at a given location. As with transverse waves, the frequency
of a sound wave is the number of cycles completed per second.
Concept 3 illustrates the motion of an individual particle in a sound wave. Refresh the
browser page to see an animation of the particle's motion. The particle oscillates back
and forth horizontally as regions of high and low pressure pass by, also horizontally.
The particle is first pushed to the right as an area of higher pressure passes, and then
pulled to the left by a region of lower pressure. As high and low pressure regions pass
by, the individual particles oscillate in simple harmonic motion.
The harmonic oscillation of the particles distinguishes a sound wave from wind. Wind
causes particles to have net displacement; it moves them from one location to another.
There is no net movement of air particles over time due to sound waves. The particles
oscillate back and forth around their original locations.
Two aspects of the behavior of gas molecules will help you understand sound waves.
First, we have used increased density and increased pressure to define condensation,
and decreased density and decreased pressure to define rarefaction. Density and
pressure are correlated. The ideal gas law (which you may study in a later chapter)
states that, everything else being equal, pressure increases with the number of gas
molecules in a system. This means that the pressure is greater in regions of
condensation than in regions of rarefaction. Other factors (such as temperature) also
influence pressure, but in this discussion we treat them as constant.
Second, the speed of sound can be understood in terms of the behavior of air
molecules. The speed v of a sound wave does not equal the speed of the loudspeaker’s
motion. That may seem odd. How could the waves move faster or slower than the
object that causes them?
The diagram we use simplifies the nature of the motion of air molecules in a wave. Air molecules at room temperature move at high speeds
(hundreds of meters per second) and frequently collide. On average, their location is stationary since their motion is random, so we can draw
them as stationary to reflect their average position. On the other hand, they are always moving, and when the loudspeaker moves, it changes
the velocity of molecules that are already in motion. The change in velocity caused by the loudspeaker is transmitted through the air by multiple
collisions as a function of the random speeds of the molecules. The faster the molecules are moving, the more frequently they will collide. As
the air becomes warmer, for example, the average thermal speed of the molecules increases, as does the speed of sound. Properties of the
medium itself, not the speed of the loudspeaker, determine the speed of sound.
Structure of a sound wave
Condensation, followed by rarefaction
Particles in a sound wave
Move in simple harmonic motion
16.2 - Human perception of sound frequency
When a sound wave composed of alternating high and low pressure regions reaches a
human ear, the wave vibrates the eardrum, a thin membrane in the outer ear. The
vibrations are then carried through a series of structures to generate signals that are
transmitted by the auditory nerve to the brain, which interprets them as sound.
There is a subjective relationship between the frequency of a sound wave and the pitch
of the sound you hear. Pitch is the distinctive quality of the sound that determines
whether it sounds relatively high or low within a range of musical notes. A home smoke
alarm issues a high-pitched beep, while a foghorn emits a low-pitched rumble. The
human ear is extremely sensitive to differences in the frequency of sound waves.
Apure tone sound consists of a sound of a single frequency. The tones produced by
musical instruments combine waves with several frequencies, but each note has a
fundamental frequency that predominates. The note middle C on a piano has a
fundamental frequency of 262 cycles per second (Hz); the lowest and highest notes of a
piano have frequencies of 27.5 and 4186 Hz, respectively. Orchestras tune to a note of
440 Hz (the A above middle C). To experiment with frequency and pitch yourself, try the
interactive simulation in the next section.
A young person can hear sounds that range from 20 to 20,000 Hz. With age, the ability of humans to perceive higher frequency sounds
diminishes. Middle-aged people can hear sounds with a maximum frequency of about 14,000 Hz.
The human ear is sensitive to a wide range of frequencies, but other animals can perceive frequencies that humans cannot. Whales emit and
hear sounds with a frequency as low as 15 Hz. Bats emit sounds in a frequency range from 20,000 Hz up to 100,000 Hz and then listen to the
reflected sound to locate their prey. Dogs (and cats) can detect frequencies more than twice as high as humans can hear, and some dog
whistles operate at frequencies that the animals can hear but humans cannot.
Interestingly, when it comes to certain sounds, the ear is not the most sensitive part of the human body. Sometimes you can feel sounds even
when you cannot hear them. Some contrabass musical instruments are designed to play notes below the lowest limit of human hearing
(20 Hz). For example, the organ in the Sydney (Australia) Town Hall can play a low, low C that vibrates at only 8 Hz, a rumbling that can only