Suppose a researcher is considering using the interference of ultrasonic waves to deposit energy at speciffic locations in the human body for therapeutic purposes. To est their ideas, they setup the apparatus shown in the diagram below, where two ultrasonic transducers project in-phase ultrasonic waves with the same amplitude and requency into a sample that is designed to mimic the properties of human tissue. A Sa Sample 'our job is to help the researcher fınd a frequency in the range of 1MHZ-10MHZ that would deposit large energy at location A (via constructive interference) and leposit no energy at location B (via complete destructive interference.) The locations are specified geometrically in the figure, where d= 6.4cm. Take the speed of sound ultrasonic waves) in the sample to be 1,454m/s (which is quite similar to the speed of sound in human tissue.)
Suppose a researcher is considering using the interference of ultrasonic waves to deposit energy at speciffic locations in the human body for therapeutic purposes. To est their ideas, they setup the apparatus shown in the diagram below, where two ultrasonic transducers project in-phase ultrasonic waves with the same amplitude and requency into a sample that is designed to mimic the properties of human tissue. A Sa Sample 'our job is to help the researcher fınd a frequency in the range of 1MHZ-10MHZ that would deposit large energy at location A (via constructive interference) and leposit no energy at location B (via complete destructive interference.) The locations are specified geometrically in the figure, where d= 6.4cm. Take the speed of sound ultrasonic waves) in the sample to be 1,454m/s (which is quite similar to the speed of sound in human tissue.)
College Physics
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Author:Raymond A. Serway, Chris Vuille
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Chapter1: Units, Trigonometry. And Vectors
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Transcribed Image Text:Suppose a researcher is considering using the interference of ultrasonic waves to deposit energy at specific locations in the human body for therapeutic purposes. To
test their ideas, they setup the apparatus shown in the diagram below, where two ultrasonic transducers project in-phase ultrasonic waves with the same amplitude and
frequency into a sample that is designed to mimic the properties of human tissue.
Sample
Your job is to help the researcher find a frequency in the range of 1MHZ-10MHZ that would deposit large energy at location A (via constructive interference) and
deposit no energy at location B (via complete destructive interference.) The locations are specified geometrically in the figure, where d= 6.4cm. Take the speed of sound
(ultrasonic waves) in the sample to be 1,454m/s (which is quite similar to the speed of sound in human tissue.)
Write an explanation to the researcher showing your reasoning and calculations.
(hint: First, write the conditions for constructive and destructive interference in terms of the frequency (well, write them in terms of the wavelength then find a way to substitute for wavelength in terms
of frequency.) Then, algebraically re-arrange the expressions in terms of the frequencies. Then find a frequency within the given range that satisfies the conditions. Also, pay attention to the units, and
recall that 1MHZ = 1 million cycles per second.)
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