R The figure above shows a transmitter and a receiver of sound waves contained in a single instrument. It is used to measure the speed u of a target object (idealized as a flat plate) that is moving directly toward the unit, by analyzing the waves reflected from the target. Show that the frequency f. of the reflected waves at the receiver is related to their source frequency f, by V + u f, = f, V – u where v is the speed of the waves. In great many practical situations, u << v. In that case, show that the equation above becomes: f,-f, 2u IS %3D V

Classical Dynamics of Particles and Systems
5th Edition
ISBN:9780534408961
Author:Stephen T. Thornton, Jerry B. Marion
Publisher:Stephen T. Thornton, Jerry B. Marion
Chapter13: Continuous Systems; Waves
Section: Chapter Questions
Problem 13.19P
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The figure above shows a transmitter and a receiver of sound
waves contained in a single instrument. It is used to measure the
speed u of a target object (idealized as a flat plate) that is
moving directly toward the unit, by analyzing the waves
reflected from the target.
Show that the frequency f. of the reflected waves at the receiver
is related to their source frequency f, by
V + u
f, f,
V -u
where v is the speed of the waves.
In great many practical situations, u << v. In that case, show that
the equation above becomes:
f,-f,
2u
f.
V
IS
In medical diagnosis using ultrasound it is said " For every mm
per second that a structure in the body moves, the incident
ultrasound wave is shifted by approximately 1.30 Hz per MHz".
What speed of the ultrasound waves in the tissue do you deduce
from this statement?
Transcribed Image Text:R The figure above shows a transmitter and a receiver of sound waves contained in a single instrument. It is used to measure the speed u of a target object (idealized as a flat plate) that is moving directly toward the unit, by analyzing the waves reflected from the target. Show that the frequency f. of the reflected waves at the receiver is related to their source frequency f, by V + u f, f, V -u where v is the speed of the waves. In great many practical situations, u << v. In that case, show that the equation above becomes: f,-f, 2u f. V IS In medical diagnosis using ultrasound it is said " For every mm per second that a structure in the body moves, the incident ultrasound wave is shifted by approximately 1.30 Hz per MHz". What speed of the ultrasound waves in the tissue do you deduce from this statement?
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