http://www.ck12.org Chapter 11. Vibrations and Sound
Check Your Understanding
- The minimum sound intensity that a typical human ear can detect is 10−^12 Wm 2. Normal conversation occurs with a
sound intensity of about 10−^6 Wm 2 at a distance of 1.00 m between each person.
a. How far would a third person need to be from the conversation in order not to hear any sound from the
conversation?
Answer: An intensity of 10−^6 Wm 2 is one-million times greater than an intensity of 10−^12 mW 2 since^10
− 6
10 −^12 =^10
(^6) =
one million. If the intensity diminished as^1 r, we would need to be one million times farther away or one million
meters away. But the intensity diminishes asr^12 sor^2 = 106 →r= 103 or a factor of one thousand→( 1 m)× 103 =
103 m, that is one-kilometer from the source; or if you prefer^10
− 6
r^2 =^10
− (^12) →r (^2) = 106 →r= 103 →( 1 m)( 103 ) =
103 m.
This is a rather astounding result. A third person one kilometer away will be on the verge of still hearing sound
emanating from the conversation. If a person is any farther away, no sound is detectible. It must be understood
that this is possible under very controlled conditions with no other distracting or overwhelming sounds and that our
answer, in the real life, is considerably less.
The human ear is an amazing organ. The lowest intensity sound that we can hear corresponds to a vibration of
amplitude 0.3 billionths of a centimeter. Of course, there are a huge number of molecules being displaced by this
distance inside the auditory canal.
Frequency Range of Human Hearing
When we listen to a piece of music we speak of pitch, loudness and quality.We have already said that the loudness
of a sound is associated with the amplitude of the wave. Pitch is associated with thefrequencyof the sound, or the
number of cycles per second of the vibration. High pitch sounds can be painful and annoying- think of a finger nail
moving across a chalk board.
The human ear is responsive to a frequency range of about 20 Hz –20,000 Hz( 20 Kilohertz= 20 kHz). Most people
cannot hear at the very low end or the very high end of this range. Most human speech occupies the range between
500Hz - 5000 Hz.
Consonant sounds are most important in distinguishing one word from another. In the English language, distinguish-
ing words like slides and flies can be challenging to the hard-of-hearing. The s-sound in English is a high-frequency
sound, about 10 kHz. It’s also the sound we associate with electrical static. People who become hard-of-hearing
usually lose the ability to hear well at higher frequencies and many s-sounds are either lost or misheard.
The ear can also distinguish between the sounds that have the same frequency and intensity. For example, most
people can tell the difference between a c-note played on two different musical instruments. This is called the
quality or timbre of the sound. This is a result of resonance,which will be discussed later.
Frequencies Beyond Human Hearing
Modern technology has found ways of using sounds that the human ear is incapable of hearing. You may be familiar
with the term sonar, which stands for "sound navigation and ranging."Sonar uses ultrasonic sound (sound waves
beyond human hearing) ranging infrequencies of 20 kHz to 100 kHz. Sonar has been used extensively in the military
in dealing with submarine warfare, seeFigure11.7. Sonar signals can detect submarines and determine their
location. Since the velocity of sound in water is known, half of the round-trip time of travel of the signal is the
distance to the submarine. Sonar is also used in mapping the ocean bottom, commercial fishing, determining the
extent of icebergs under water, and mapping geologic strata. Higher frequency ultrasonic waves are used in medicine.
Figure11.8 shows an ultrasound of a baby.