be felt by the audience members. Low frequency sounds are also used in movies and some arcade games to increase tension and suspense.

16.3 - Interactive problem: sound frequency

In this interactive simulation, you can experience the relationship between sound

wave frequency and pitch.

The simulation includes a virtual keyboard. (As you might expect, your computer

must have a sound card and speakers or a headphone for you to be able to hear

the musical notes.)

Above the keyboard is an oscilloscope, used to display the sound wave. The

oscilloscope graphs the waves with time on the horizontal axis. Each division on the

horizontal axis represents one millisecond.

On the vertical axis, the oscilloscope graphs an air particle’s displacement from

equilibrium as a function of time, as the sound wave passes by. The wave is

longitudinal, and peaks and troughs on the graph correspond to the particle’s

maximum displacement, which occurs along the direction of the wave’s motion.

Although we do not provide units on the vertical axis, displacements of the particles

in audible sound waves are generally in the micrometer range.

The frequency of ordinary musical notes is high enough that the oscilloscope graphs

time in milliseconds. The middle C on the keyboard (a white key near its midpoint) has a frequency of about 262 Hz (cycles per second), or

0.262 cycles per millisecond. A full cycle of this sound wave would span slightly less than four squares on the horizontal axis of the

oscilloscope.

When you start the simulation, the instrument is set to "synthesizer." When you press a key, you will hear a tone that plays at the same

intensity for as long as you hold down the key. Even this simple synthesizer tone consists of several frequencies, but one fundamental

frequency predominates, and it is displayed on the oscilloscope.

You can use the oscilloscope to compare the frequencies of various sound waves, as well as using your ears to compare various pitches. Do

they relate? Specifically, do higher pitched musical notes have a higher or lower frequency than lower pitched musical notes? If you know how

to play notes on the piano that are an octave apart, compare the frequencies and wavelengths of these sounds. What are the relationships?

You can also set the simulation to hear notes from a grand piano. These tones are even more complex than the synthesizer and again we

display just the fundamental frequency. To simulate a piano's sound, the notes will fade away even if you hold down the key, but the

oscilloscope will continue to display the initial sound wave.

This simulation is designed to give you an intuitive sense of the frequencies of different musical notes. If you know how to play the piano, even

something as simple as "Chopsticks," play a song and observe the waves that make up that tune. You can also play a note and see how close

a friend can come to guessing it. Some people have a capability called perfect pitch, and can tell the note or frequency correctly every time.

16.4 - Sound intensity

Sound intensity: The sound power per unit area.

Sound carries energy. It may be a small amount, as when someone whispers in your

ear, or it may be much more, as when the sonic boom of an airplane rattles windows, or

when a guitar amplifier goes to 11.

Sound intensity is used to characterize the power of sound. It is defined as the power of

the sound passing perpendicularly through a surface area. Watts per square meter are

typical units for sound intensity.

The definition of sound intensity is shown in Equation 1. An intensity of approximately

1×10í^12 W/m^2 is the minimum perceptible by the human ear. An intensity greater than

1 W/m^2 can damage the ear.

As a sound wave travels, it typically spreads out. You perceive the loudness of the

sound of a loudspeaker at an outdoor concert differently at a distance of one meter than

you do at 100 meters. The intensity of the sound diminishes with distance.

Equation 2 is used to calculate the intensity of sound when it spreads freely from a

single source. The intensity diminishes with the square of the distance from the source.

It does so because the sound energy in this case is treated as being distributed over the surface of a sphere whose radius increases with time.

The denominator of the expression for intensity is 4 ʌr^2 , the expression for the surface area of a sphere.

The example problem to the right asks you to find the relative sound intensities experienced by two listeners, one twice as far as the other from

the fireworks. In this scenario, the sound is four times as intense for the closer listener, but this does not mean he hears the sound as four

times louder. The loudness of sounds as perceived by human beings has a logarithmic relationship to sound intensity. This topic is explored in

another section.

Here we have focused on sound that freely expands in all directions. However, sound can also reflect off surfaces such as walls. Concert halls

are designed to take advantage of this reflection to deliver a full, rich sound to the audience.

Sound intensity

Sound power that passes

perpendicularly through a surface area

Diminishes with square of distance from

sound source

(^310) Copyright Kinetic Books Co. 2000-2007 Chapter 16