A trainer at a dog show lifts a small silver whistle and blows hard. You hear nothing at all. Yet the dog across the ground turns at once and runs to her. The whistle made a sound, and it was loud enough for the dog. It was simply not a sound that a human ear can hear.
The range of frequencies
Human hearing is limited both in frequency and in intensity. For most healthy young listeners, the audible frequency range extends from approximately \(20\,\text{Hz}\) to \(20\,\text{kHz}\). This is the audible range. Frequencies below \(20\,\text{Hz}\) are called infrasound, whereas frequencies above \(20\,\text{kHz}\) are called ultrasound.
Press Listen in the figure above and slide the frequency up slowly. Many adults stop hearing the tone somewhere between \(15\) and \(18\,\text{kHz}\), because the upper limit falls with age. At the low end, small speakers cannot produce the deepest tones well. The wavelengths in air run from \(340/20 = 17\,\text{m}\) at the bottom of the range to \(1.7\,\text{cm}\) at the top.
A dog whistle produces a sound of about \(25\,\text{kHz}\). What kind of sound is this for a human listener?
Elephants call to each other over several kilometres with rumbles as low as \(15\,\text{Hz}\). What kind of sound is this for a human listener?
A hospital ultrasound scanner sends pulses of a few megahertz into the body and listens for their echoes. At \(3\,\text{MHz}\) the wavelength in soft tissue, where sound travels at about \(1500\,\text{m/s}\), is only half a millimetre. Such short waves reflect from small structures, so the echoes draw a picture of a baby in the womb. Bats use the same idea at about \(20\) to \(100\,\text{kHz}\) to hunt insects in the dark.
The range of intensities
The faintest sound that can be heard under ideal conditions has an intensity of about \(I_0 = 1.0 \times 10^{-12}\,\text{W/m}^2\). This corresponds to \(0\,\text{dB}\) on the decibel scale and is known as the threshold of hearing. It is the reference intensity of lesson 4.
At the other extreme, an intensity of order \(1\,\text{W/m}^2\), around \(120\,\text{dB}\), marks the threshold of pain. Prolonged exposure to sound levels near this intensity can permanently damage hearing. The ear spans a factor of \(10^{12}\) in intensity between these two thresholds.
The perception of sound is therefore shaped by two things. One is how much power per unit area reaches the ear, the intensity. The other is whether that power lies within the audible frequency band. A very intense sound at \(30\,\text{kHz}\) is still unheard.
The threshold of hearing depends on the frequency. \(I_0 = 10^{-12}\,\text{W/m}^2\) is the value near \(1\) to \(4\,\text{kHz}\), where the ear is most sensitive. At \(50\,\text{Hz}\) a tone must be tens of decibels more intense to be heard at all. That is why a sound meter often uses a weighting, marked dB(A), which counts low and very high frequencies for less.
Which of these sounds can a healthy young listener hear?
Common sound levels
Here are some common sound levels, from the faintest to the most dangerous.
- 0 dB: threshold of hearing
- 30 dB: whisper
- 60 dB: normal conversation
- 90 dB: heavy traffic
- 120 dB: threshold of pain
- 140 dB: jet engine at close range
Read the ladder of Fig 5.1 in steps. From a whisper to normal conversation is \(30\,\text{dB}\), a factor of \(10^3\) in intensity. From conversation to heavy traffic is another \(10^3\). The jet engine at \(140\,\text{dB}\) delivers \(100\,\text{W/m}^2\), a hundred times the threshold of pain.
Distance and level
The level of a sound falls as you move away from it. For a point source the intensity falls as \(1/r^2\), by the inverse-square law of lesson 3. Each doubling of the distance divides the intensity by \(4\), a fall of \(10\log_{10}4 = 6\,\text{dB}\). Ten times the distance divides it by \(100\), a fall of \(20\,\text{dB}\).
If the distance from a point source is tripled, the intensity
A truck horn gives a sound level of \(90\,\text{dB}\) at \(2\,\text{m}\). Treat it as a point source in open air. What is the level at \(20\,\text{m}\), in dB?
The Noise Pollution (Regulation and Control) Rules of 2000 set limits on sound levels in India. In a residential area the limit is \(55\,\text{dB}\) by day and \(45\,\text{dB}\) at night. Near a hospital, school or court, a silence zone, it is \(50\,\text{dB}\) by day and \(40\,\text{dB}\) at night. The same rules forbid loudspeakers in the open between 10 p.m. and 6 a.m., except in a few permitted cases.
Pitch, loudness and quality
The ear tells apart three characteristics of a musical note. The first is pitch, how high or low the note sounds. It is set by the frequency, and a higher frequency gives a higher pitch. The second is loudness, how strong the note sounds. It is set mainly by the intensity, which the sound level in decibels measures.
The third is quality, also called timbre. A sitar and a flute can play the same note at the same loudness, and still you can tell them apart. Each instrument sounds the note with its own mix of harmonics. These are tones at whole-number multiples of the lowest frequency, \(f_1\), \(2f_1\), \(3f_1\) and so on. The mix gives the waveform its shape, and the ear hears that shape as the quality.
Listen to Fig 5.2 and change the chip. The period of the wave never changes, so the pitch stays the same. Only the shape changes, and with it the quality. The pure tone sounds dull, like a tuning fork. The odd harmonics sound hollow, like a clarinet. A clarinet is a pipe closed at one end, and such a pipe cannot sound the even harmonics. The chapter Standing Sound Waves shows why.
A sitar and a flute play the same note at the same sound level. You can still tell which is which. In what do the two sounds differ?
Now return to the dog whistle. It was loud enough, well above the threshold of hearing. But its frequency lay above \(20\,\text{kHz}\), outside the audible band of a human ear. A dog hears up to about \(45\,\text{kHz}\), so for the dog it was a clear call.
- Thinking a very intense sound must be audible.Its frequency must also lie between \(20\,\text{Hz}\) and \(20\,\text{kHz}\).
- Mixing up infrasound and ultrasound.Infrasound is below \(20\,\text{Hz}\); ultrasound is above \(20\,\text{kHz}\).
- Taking the level to fall in proportion to distance.For a point source, each doubling of distance lowers the level by \(6\,\text{dB}\), and ten times the distance by \(20\,\text{dB}\).
- Linking quality to loudness.Quality is set by the mix of harmonics. Two sounds of the same pitch and loudness can differ in quality.