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occurs through sound waves when it is not clear what is hap-
TABLE 5.2
pening. A truck drives down the street, for example, and one
Comparison of noise levels in decibels with intensity window rattles but the others do not. A singer shatters a crystal
Intensity water glass by singing a single note, but other objects remain
Example Response Decibels W/m 2 undisturbed. A closer look at the nature of vibrating objects and
the transfer of energy will explain these phenomena.
Least needed for Barely 0 1 × 10 –12
hearing perceived Almost any elastic object can be made to vibrate and will
vibrate freely at a constant frequency aft er being suffi ciently dis-
Calm day in Very, very 10 1 × 10 –11
woods quiet turbed. Entertainers sometimes discover this fact and appear
Whisper (15 ft) Very quiet 20 1 × 10 –10 on late-night talk shows playing saws, wrenches, and other
odd objects as musical instruments. All material objects have
Library Quiet 40 1 × 10 –8
a natural frequency of vibration determined by the materials
Talking Easy to hear 65 3 × 10 –6
and shape of the objects. The natural frequencies of diff erent

Heavy street Conversation 70 1 × 10 –5
traffic difficult wrenches enable an entertainer to use the suspended tools as if
they were the bars of a xylophone.
Pneumatic drill Very loud 95 3 × 10 –3
(50 ft) If you have ever pumped a swing, you know that small
forces can be applied at any frequency. If the frequency of the
Jet plane (200 ft) Discomfort 120 1
applied forces matches the natural frequency of the moving
swing, there is a dramatic increase in amplitude. When the two
frequencies match, energy is transferred very effi ciently. Th is
condition, when the frequency of an external force matches the
wave is not a linear relationship. In fact, a sound that is perceived natural frequency, is called resonance. The natural frequency of

as twice as loud requires 10 times the intensity, and quadrupling an object is thus referred to as the resonant frequency, that is, the
the loudness requires a 100-fold increase in intensity. frequency at which resonance occurs.
The human ear is very sensitive. It is capable of hearing A silent tuning fork will resonate if a second tuning fork

2
sounds with intensities as low as 10 −12 W/m and is not made with the same frequency is struck and vibrates nearby ( Figure 5.19).
uncomfortable by sound until the intensity reaches about You will hear the previously silent tuning fork sounding if you
2
12

1 W/m . The second intensity is a million million (10 ) times stop the vibrations of the struck fork by touching it. Th e waves
greater than the first. Within this range, the subjective inter- of condensations and rarefactions produced by the struck tuning

pretation of intensity seems to vary by powers of ten. Th is obser- fork produce a regular series of impulses that match the natural

vation led to the development of the decibel scale to measure the frequency of the silent tuning fork. This illustrates that at reso-
intensity level. The scale is a ratio of the intensity level of a given nance, relatively little energy is required to start vibrations.

–12
2
sound to the threshold of hearing, which is defined as 10 W/m A truck causing vibrations as it is driven past a building

at 1,000 Hz. In keeping with the power-of-ten subjective interpre- may cause one window to rattle while others do not. Vibrations
tations of intensity, a logarithmic scale is used rather than a linear caused by the truck have matched the natural frequency of this
scale. Originally, the scale was the logarithm of the ratio of the window but not the others. The window is undergoing reso-

intensity level of a sound to the threshold of hearing. Th is def- nance from the sound wave impulses that matched its natural
inition set the zero point at the threshold of human hearing. frequency. It is also resonance that enables a singer to break a
The unit was named bel in honor of Alexander Graham Bell water glass. If the tone is at the resonant frequency of the glass,

(1847–1922). This unit was too large to be practical, so it was the resulting vibrations may be large enough to shatter it.

reduced by one-tenth and called a decibel. The intensity level of a
sound is therefore measured in decibels ( Table 5.2). Compare the
decibel noise level of familiar sounds listed in Table 5.2, and note
that each increase of 10 on the decibel scale is matched by a mul-
tiple of 10 on the intensity level. For example, moving from a deci-
bel level of 10 to a decibel level of 20 requires 10 times more inten- Struck tuning fork Not struck, but
sity. Likewise, moving from a decibel level of 20 to 40 requires a vibrating, tuning
fork
100-fold increase in the intensity level. As you can see, the decibel
scale is not a simple linear scale.
RESONANCE
You know that sound waves transmit energy when you hear a
thunderclap rattle the windows. In fact, the sharp sounds from
FIGURE 5.19 When the frequency of an applied force, including
an explosion have been known to not only rattle but also break the force of a sound wave, matches the natural frequency of an

windows. The source of the energy is obvious when thunder- object, energy is transferred very efficiently. The condition is called
claps or explosions are involved. But sometimes energy transfer resonance.

128 CHAPTER 5 Wave Motions and Sound 5-14