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Objective: To identify whether positive, negative, or zero work is being done, to identify the force that is doing the work, and to describe the energy transformation associated with such work.

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The deciBel Scale

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Use provided data to determine the basic relationships between the distance from the source, the intensity, and the decibel rating of a sound.

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Use your data mining skills to relate intensity, deciBel rating, and distance from the source for two different locations.

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Use provided data to relate the deciBel rating of two sounds to the intensity of the same two sounds.

Basic Relationships

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Intensity and deciBels

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Intensity and the deciBel System A source of sound produces sound energy that propagates outward from the source in roughly all directions. The rate at which this sound energy is produced is known as the power. A 300 Watt speaker (operating at 100% efficiency) produces 300 Joules of sound energy every second. The rate at which this sound energy reaches a given cross-sectional area is known as the sound intensity. Sound intensity is measured in units of power per area - for example, Watts per meter squared. The intensity of sound from a source varies with the distance from the source. Table 1 portrays the relationship between sound intensity and the distance from a 300-Watt audio speaker. Humans are able to detect sound with an intensity as low as 1.0 x 10-12 W/m2. This particular intensity level is known as the threshold of hearing (TOH). Many humans can hear sounds that are 10 trillion times more intense than the TOH without exhibiting signs of pain. Given the large range of intensities that humans are sensitive too, it is common to express the sound intensity using a logarithmic scale known as the decibel scale. A decibel is one-tenth of a Bel and a Bel is the logarithm of the ratio of two sound intensity values. In acoustics, the decibel rating assigned to a sound is the logarithm of the ratio of the intensity of that sound to the intensity of the threshold of hearing. This logarithmic relationship is illustrated in Table 2. High intensity sounds can cause permanent damage to the human ear. Decibel levels of 120 dB can cause pain to the ears of some humans. Researchers studying hearing loss claim that prolonged exposure to sound levels of 85 dB can lead to hearing loss. They suggest limiting exposure to sound levels that exceed 100 dB to no more than 15 minutes. Exposure to sound levels of 110 dB should be restricted to 1-minute duration. Teenagers are most susceptible to damage by exposure to loud music emanating from the earbuds or exposure to loud sounds at concerts. Figure 1 shows the dependence of the decibel level upon the distance from the 3000-Watt super-speakers used at a concert.

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Stopping Distance One aspect of safe driving involves the ability to stop a car readily. This ability depends upon the driver's alertness and readiness to stop, the conditions of the road, the speed of the car, and the braking characteristics of the car. The actual distance it takes to stop a car consists of two parts - the reaction distance and braking distance. When a driver sees an event in his/her field of view that might warrant braking (for example, a dog running into the street), a collection of actions must be taken before the braking actually begins. First the driver must identify the event and decide if braking is necessary. Then the driver must lift his/her foot off the gas pedal and move it to the brake pedal. And finally, the driver must press the brake down its full distance in order to obtain maximum braking acceleration. The time to do all this is known as the reaction time. The distance traveled during this time is known as the reaction distance. Once the brakes are applied, the car begins to slow to a stop. The distance traveled by the car during this time is known as the braking distance. The braking distance is dependent upon the original speed of the car, the road conditions, and characteristics of the car such as its profile area, mass and tire conditions. Figure 1 shows the stopping distance for a Toyota Prius on dry pavement resulting from a 0.75-second reaction time. The reaction time of the driver is highly dependent upon the alertness of the driver. Small changes in reaction time can have a large effect upon the total stopping distance. Table 1 shows the reaction distance, braking distance, and total stopping distance for a Toyota Prius with an original speed of 50.0 mi/hr and varying reaction times.