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Sound Intensity and Intensity Level. Homework #3 Friday’s Standing Wave Lab will be due Friday. Alexander Graham Bell. Photo taken 1914 to 1919.
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Sound Intensity and Intensity Level Homework #3 Friday’s Standing Wave Lab will be due Friday.
Alexander Graham Bell Photo taken 1914 to 1919 Bell's father, grandfather, and brother had all been associated with work on elocution and speech, and both his mother and wife were deaf, profoundly influencing Bell's life's work.[ Bell considered his most famous invention an intrusion on his real work as a scientist and refused to have a telephone in his study. Bell became one of the founding members of the National Geographic Society
Sound: Intensity and Intensity Level I. Sound Intensity loudness or “volume” Intensity of sound is the ____________________ of the sound. Sound propagates through the air via fluctuations in pressure of the gas carrying the sound. The greater the amplitude of the fluctuations in the pressure, the louder the sound appears. Intensity is defined equal to the amount of energy transferred per second through the sound wave divided by the area through which the energy passes.
The size of the area depends on the distance from the source. Imagined surface surrounding the sound source. All sound from the source must pass through the area as the sound energy expands out. Intensity is the rate of flow of sound energy per unit of area.
Image shows sound expanding our from a source. The shaded region is the (imagined) area through which the sound energy passes.
This shows an ideal source of sound energy. The energy spreads uniformly in all directions (spherical symmetry). This is called an isotropic source of sound.
Intensity is calculated by dividing the power, in watts, by the cross-sectional area, in m2, through which the sound travels. The formula is: Here, I is the intensity in W/m2, P is the power in watts, and A is the area, in m2, through which the sound travels.
Some useful values for reference are related to human hearing. The least amount of sound intensity that the average human ear can perceive, averaged over frequency, is 10-12 W/m2. This value is usually known as the threshold of hearing, and has the symbol Io. On the other end of the spectrum is the greatest intensity the average human ear can withstand without pain. This value is on the order of 1 W/m2. This is called the threshold of pain. (Values on the table are given in decibels.)
Typical response of human ear to sound levels. 0 dB represents the threshold of hearing.
Example #1: A sound wave has a power of 14.0 W as its passes through an area that measures 49.0 cm by 20.0 cm. (a) What is the intensity of this sound wave?
(b) If this sound wave entered your ear canal at this same intensity, what would be the rate energy is transferred from the sound wave to your ear drum? Assume the diameter of your ear canal is 5.00 mm.
II. Spherical Distributions of Sound Waves: Intensity When sound is emitted by a source, the energy of the sound wave spreads in all direction. By the conservation of energy, the total amount of sound energy is fixed. As the sound spreads farther from the source, it passes through successively greater areas. The intensity drops as the sound travels away from the source. The formula for the intensity of sound, I, as a function of distance from the source, r, is: A source of sound that spreads the sound outwards equally in all directions is known as an isotropic source. The above equation is valid for isotropic sources.
Example #2: At a distance of 36.0 meters from an isotropic source, sound is measured to carry energy at a rate of 90.0 W. (a) What is the intensity of the sound at this location?
(b) At what distance from the source would the sound be at the threshold of pain, 1 W/m2?
III. Sound Intensity Level As can be seen in the examples above, the intensity of sounds varies over a great range of values. Even for the human ear, this ranges form 10-12 W/m2 to 1 W/m2. Dealing with these differences in order of magnitude is often frustrating, making direct comparisons difficult. A new scale, similar to the pH scale, is needed to put these values in a range that easier to form comparisons. The intensity level scale makes this possible: b is the symbol for intensity level, measured in decibels or dB. I is the intensity of the wave to be studied, and Io is the threshold of hearing, 10-12 W/m2.
Example #3: What is the decibel level or intensity level of (a) the threshold of hearing and (b) the threshold of pain?
Example #4: (a) If the intensity level of a jet aircraft engine is 150 dB, what is the intensity of the engine?
(b) If this value is measured at a distance of 50.0 m from the aircraft, what is the rate at which sound energy is produced by the jet engine?
Example #5: In a business office, the typewriters are rated at 72 dB intensity level each. How many typewriters can run at any given instant and not exceed the maximum of 85 dB as established by OSHA? Only intensities, I, are additive. Convert to intensity.
The total number of machines that may run at any given time is the ratio of the two intensities:
Example #6: A local ordinance in the city of Torrance limits sounds produced by any motorized vehicle to be under 83 dB when measured at a distance of 15.0 m from the source. A policeman measures the sound output of a car’s stereo system to be 77.0 dB at 90.0 meters distance. Is this car in violation of the sound ordinance? This is the intensity of the sound at a distance of 90.0 m. Now calculate to the intensity at 15.0 m.
This is the intensity of the sound at a distance of 15.0 m. Now find the intensity level for this sound level.
This exceeds the intensity level set by the local ordinance.
