Sound pressure level
In a sound wave there are extremely small periodic variations in atmospheric pressure to which our ears respond in a rather complex manner. The minimum pressure fluctuation to which the ear can respond is less then one billionth (10-9) atmospheric pressure. This threshold of audibility, which varies from person to person, corresponds to a sound pressure amplitude of about 2 x 10-5 N/m2 (Newton’s/meter 2 ) at a frequency of 1000 Hz. The threshold of pain corresponds to pressure amplitude approximately one million (106 ) times greater, but still less than 1/1000 of atmospheric pressure.
A sound level meter, consisting of a microphone, an amplifier and a meter that reads in decibels, measures sound pressure levels. Sound pressure levels of a number of sounds are given in Table 2. Class exercise: students can obtain a feeling for different sound pressure levels by using a sound level meter.
Table 2 Typical Sound Levels
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Jets take off (60 Meters)
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120 dB
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Construction site 110 dB intolérable
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Shout (1.5 meters)
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100 dB
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Heavy truck (15meters)
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90 dB very noisy
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Urban street 80 dB
Automobile interior 70 dB noisy
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Normal conversation (1 meter)
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60 dB
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Office, classroom
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50 dB moderates
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Living room 40 dB
Bedroom at night 30 dB quiet
Broadcast studio 20 dB
Rustling leaves 10 dB barely
audible4
The word sound is used to describe two different things: (1) and auditory sensation in the ear and (2) the disturbance in a medium which can cause a sensation.
Think of all the sounds that you’ve heard since you awoke this morning. Did you hear a blaring alarm, honking horns, human voices, and lockers slamming? Your ears allow you to recognize these different sounds. These sounds all have one thing in common. The vibration of objects produces them all. The vibrations of your vocal cords produce voice. The energy produced by these vibrations is carried to your friend’s ear by sound waves traveling through a medium, air.
The speed of sound waves depends on the medium through which the wave travels and it temperature. Air is the most common medium you hear sound waves through, but sound waves can be transmitted through any type of matter. Liquids and solids are even better conductors of sound than air because the individual particles in a liquid or solid are much closer together than the particles in air.
Sound waves transmit energy faster in substances with smaller spaces between the particles. A research question for students: Can sound be transmitted if there is no matter? Astronauts on the moon would find it impossible to talk to each other without the aid of modern electronic communication systems. Since the moon has no atmosphere, there is no air to compress or expand.
The temperature of the medium is also an important factor in determining the speed sound travels. As the temperature of the substance increases, the molecules move faster and collide more frequently. This increase in molecule collisions transfers energy more quickly. Sound travels through air at 344 miles/second if the temperature is 20o C, but only 332 miles/second when the temperature is 0o C.
To better understand sound waves, consider a large pipe or tube with a loudspeaker at one end. Although sound waves in this tube are similar in many respects to the waves on a rope, they are more difficult to visualize, because we cannot see the displacement of the air molecules as the sound wave propagates. The pulse of air pressure travels down the tube at a speed of about 340 miles/second. It may be absorbed at the far end of the tube, or it may reflect back toward the loudspeaker (as a positive pulse or a negative pulse), depending on what is at the far end of the tube.
Reflection of a sound pulse in a pipe for three different end conditions is illustrated in Figure 5. If the end is open, the excess pressure drops to zero and the pulse reflects back as a negative pulse of pressure as shown in Figure 5b; this is similar to the “fixed end” condition.
In an actual tube with an open end, a little of the sound will be radiated; most of it however, will be reflected as shown. If the end is closed, the pressure builds up to twice its value, and the pulse reflects back as a positive pulse of pressure; this condition shown in Figure 5c is similar to the “free end” reflection. If the end is terminated with a sound absorber, Figure 5d, there is virtually on reflected pulse. Such a termination is called “no echo.”
Table 1 Speed of sound in various materials
Temperature Speed
Substance 0 meters/sec. Feet/sec.
Air 0 331.3 1087
Air 20 343 1127
Helium 0 970 3180
Carbon Dioxide 0 258 846
Water 0 1410 4626
Methyl Alcohol 0 1130 3710
Aluminum - 5150 16,900
Steel - 5100 16,700
Brass - 3840 11,420
Lead - 1210 3970
Glass - 3700-5000 12 – 16,0005
Wave movements in two and three dimensions
So far we have discussed only waves that travel in one direction (ex. along a rope or in a pipe). One-dimensional waves of this type are a rather special case of wave motion. Often, waves travel outward in two or three dimensions from a source.
Water waves are an example of two-dimensional waves. Many waves can be studied conveniently by means of a ripple tank in a laboratory. A ripple tank uses a glass-bottom tray filled with water; light projected through the tray forms an image of the wave on a large sheet of paper or on a projection screen. If the materials were readily available, this would be an excellent exercise for the students. Many calculations could be performed from the data collected.
Three-dimensional waves are difficult to make visible. For this unit we will not explore the techniques used to identify 3-dimension waves.
Multiple sources of sound
Sometimes we are concerned with more than one source of sound. The way in which sound levels add may seem a little surprising at first. For example, two different sources each of which would produce a sound level of 80 dB at a certain point will together give 83 dB at that point. Figure 6 gives the increase in sound level due to additional equal sources. It is not difficult to see why this is the case, since doubling the sound power raises the sound power level by 3 dB, and thus raises the sound pressure level 3 dB. Under some conditions, however, there may be interference between waves from the two sources and the doubling relationship will not hold true.
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A Science and Math activity: The timer at a track meet starts the watch when he hears the sound of the gun rather than when he sees the flash of the gun being fired. If the gun were 200 m away from him, how much faster or slower would the recorded time be than the actual time?
SOLUTION: The speed of light is 300,000,000 m/s, so the light gets there virtually instantaneously. The speed of sound is about 330 m/s, so the timed speed will be 0.3 s faster than the real speed.
A Science and writing activity: You have just formed a new company, Ultrasonic Unlimited. Develop an advertisement for a product that uses this sound energy. SOLUTION; an encyclopedia will describe many uses including scientific, industrial, medical and residential.
Intensity and Loudness
The intensity of a sound wave depends on the amount of energy in each wave. This, in turn, corresponds to the wave’s amplitude. Intensity of a sound wave increases as its amplitude increases.
Loudness is the human perception of sound intensity. The higher the intensity and amplitude, the louder the sound. The intensity of a sound is measured in units called decibels (dB). Sounds with intensities above 120 dB may cause pain and hearing loss. Prolonged noise above 150 dB can cause permanent deafness. The roar of a racing car can be 125 dB, amplified music as high as 130 dB, and some toy guns 170 dB. Figure 7 shows some familiar sounds and their intensities in dB.
