Question

Expectant parents are thrilled to hear their unborn baby's heartbeat, revealed by an ultrasonic motion detector. Suppose the fetus's ventricular wall moves in simple harmonic motion with amplitude 1.83 mm and frequency 106 beats per minute. The motion detector in contact with the mother's abdomen produces sound at precisely 2 MHz, which travels through tissue at 1.50 km/s.

(a) Find the maximum linear speed of the heart wall. ________m/s

(b) Find the maximum frequency at which sound arrives at the wall of the baby's heart. (Enter your answer to at least six significant figures.) ______Hz

(c) Find the maximum frequency at which reflected sound is received by the motion detector. (By electronically "listening" for echoes at a frequency different from the broadcast frequency, the motion detector can produce beeps of audible sound in synchrony with the fetal heartbeat. Enter your answer to at least six significant figures.) __________Hz

Answer 1

(a) Find the maximum linear speed of the heart wall. ________m/s

The amplitude equals. transformed into meters

the maximum speed is given by

where:

amplitude
angular frequency

evaluated numerically

(b) Find the maximum frequency at which sound arrives at the wall of the baby's heart. (Enter your answer to at least six significant figures.) ______Hz

doppler effect source at rest and moving observer

where

speed of sound in the source

speed detecting apparatus
Speed wall

evaluated numerically

(c) Find the maximum frequency at which reflected sound is received by the motion detector. (By electronically "listening" for echoes at a frequency different from the broadcast frequency, the motion detector can produce beeps of audible sound in synchrony with the fetal heartbeat. Enter your answer to at least six significant figures.) __________Hz

is produced again Doppler Effect

The source (wall) is mobile and the observer (detector) is at rest.

where

speed of sound in the source

speed detecting apparatus
Speed wall

evaluated numerically