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BIO Ultrasound in Medicine. A 2.00-MHz soundwave travels through a pregnant woman鈥檚 abdomen and is reflected from the fatal heart wall of her unborn baby. The heart wall is moving toward the sound receiver as the heart beats. The reflected sound is then mixed with the transmitted sound, and 72 beats per second are detected. The speed of sound in body tissue is 1500 m/s. Calculate the speed of the fatal heart wall at the instant this measurement is made.

Short Answer

Expert verified

a)=0.625mm

b)the corresponding wavelengths are 0.075 mm to 1.5 mm.

Step by step solution

01

Given Data

Frequency emitted is 2.00鈥塎贬锄

Sound鈥檚 speed is1500鈥尘/s

Number of beats per second are 72

02

Concept of the frequency of sound wave

The frequency of the sound wave is defined as the number of oscillation produced per unit time. It is given as-

f=v

where, v is the velocity , is the wavelength androle="math" localid="1655818635098" f is the frequency of sound wave.

03

Calculate the wavelength of the wave

The frequency of the ultrasound waves is by using equation f=2.40106鈥塇锄.The wavelength of the wave is =vf

=1.5103鈥尘/s2.40106鈥塇锄=0.625鈥尘m=0.625103鈥尘

04

Calculation of wavelength

Range of the frequencies isf1=1.00鈥塎贬锄 tof2=20鈥塎贬锄 . The corresponding wavelengthrole="math" localid="1655818948502" f2 to is smaller than the corresponding wavelength tof1 , according the equationrole="math" localid="1655819020395" v=位蹿 as v does not change in the same medium. So,

2=1.5103鈥尘/s20.0106鈥塇锄=0.075103鈥尘=0.075鈥尘m

1=1.5103m/s1.00106Hz=1.5103m=1.5mm

Therefore, the corresponding wavelengths are0.75mm to 1.5mm.

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