# 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.)

### College Physics

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

### College Physics

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

#### Solutions

Chapter
Section
Chapter 14, Problem 34P
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.)

Expert Solution

(a)

To determine
maximum linear speed of the heart wall

### Explanation of Solution

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 .

Substitute 12 rad/s for ω and 1

Expert Solution

(b)

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

Expert Solution

(c)

To determine
The observed frequency of returning echo.

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