A traveling wave causes a displacement of the medium?that depends on both the position ? (or ? in two or three dimensions) and time ?. The maximum displacement of the medium at any point is the amplitude ?. The intensity of a wave is a measure of how the energy in the wave is being distributed over space and time. Since the amplitude is an indicator of the wave’s energy (think of a mass on a spring undergoing harmonic oscillations – the total mechanical energy is ((1/2)??2), thenthe intensity of a wave should be related to its amplitude. In fact, the intensity of any wave is proportional to its amplitude squared: ?∝?2. a. For a sinusoidal wave on a string without any damping, consider two points on the string ?1and ?2 separated by some distance Δ?. How does the amplitude of the wave at point ?1compare to the amplitude of the wave at point ?2? What does this tell you about the intensity and the energy of the wave? Sound waves, unlike waves on a string, spread out as they travel. Because the energy of the wave is being distributed over a larger area, the intensity and amplitude of the sound waves will decrease. For a sound wave traveling equally in all directions (a spherical wave), the intensity is inversely proportional to the area of a sphere: ?∝1/(4??2). For two points that are different distances from the source of the sound waves, ?1 and ?2, the ratio of intensities at those points is ?2/?1 = ?12/?22. This is often referred to as the inverse square law. b. An ultrasound device used for medical imaging emits sound waves with a frequency of about 1 ???=1×106 ??. We will assume that the ultrasound waves travel equally in all directions. The intensity of an ultrasound wave that is 11 ?? from its source is what percent of the intensity of the same ultrasound wave when it’s only 1 ?? from its source?
4. A traveling wave causes a displacement of the medium?that depends on both the position ? (or ? in two or three dimensions) and time ?. The maximum displacement of the medium at any point is the amplitude ?. The intensity of a wave is a measure of how the energy in the wave is being distributed over space and time. Since the amplitude is an indicator of the wave’s energy (think of a mass on a spring undergoing harmonic oscillations – the total mechanical energy is ((1/2)??2), thenthe intensity of a wave should be related to its amplitude. In fact, the intensity of any wave is proportional to its amplitude squared: ?∝?2.
a. For a sinusoidal wave on a string without any damping, consider two points on the string ?1and ?2 separated by some distance Δ?. How does the amplitude of the wave at point ?1compare to the amplitude of the wave at point ?2? What does this tell you about the intensity and the energy of the wave?
Sound waves, unlike waves on a string, spread out as they travel. Because the energy of the wave is being distributed over a larger area, the intensity and amplitude of the sound waves will decrease. For a sound wave traveling equally in all directions (a spherical wave), the intensity is inversely proportional to the area of a sphere: ?∝1/(4??2). For two points that are different distances from the source of the sound waves, ?1 and ?2, the ratio of intensities at those points is ?2/?1 = ?12/?22. This is often referred to as the inverse square law.
b. An ultrasound device used for medical imaging emits sound waves with a frequency of about 1 ???=1×106 ??. We will assume that the ultrasound waves travel equally in all directions. The intensity of an ultrasound wave that is 11 ?? from its source is what percent of the intensity of the same ultrasound wave when it’s only 1 ?? from its source?
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