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College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300

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BuyFindarrow_forward

College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300
Textbook Problem

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 1.80 mm and frequency 115 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. (b) Find the maximum frequency at which sound arrives at the wall of the baby’s heart. (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.)

(a)

To determine
maximum linear speed of the heart wall

Explanation

Given Info: frequency of heart beat is 115 beats per minute

Formula to calculate the maximum linear speed of the heart wall is,

vmax=ωA

  • A is the amplitude,
  • ω is the angular frequency,

The formula for the angular frequency is,

ω=2πf

  • f is the frequency of the heat beat,

Use 2πf for ω in the expression for vmax .

vmax=(2πf)A

Substitute 115 beats per minute for f in the above expression to get ω .

ω=2π(115/min60s/min)=120rad/s

Substitute 12 rad/s for ω and 1

(b)

To determine
Maximum frequency at which sound arrives at babies’ heart.

(c)

To determine
The observed frequency of returning echo.

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