# 17.7 Ultrasound  (Page 5/10)

 Page 5 / 10

Doppler-shifted radar echoes are used to measure wind velocities in storms as well as aircraft and automobile speeds. The principle is the same as for Doppler-shifted ultrasound. There is evidence that bats and dolphins may also sense the velocity of an object (such as prey) reflecting their ultrasound signals by observing its Doppler shift.

## Calculate velocity of blood: doppler-shifted ultrasound

Ultrasound that has a frequency of 2.50 MHz is sent toward blood in an artery that is moving toward the source at 20.0 cm/s, as illustrated in [link] . Use the speed of sound in human tissue as 1540 m/s. (Assume that the frequency of 2.50 MHz is accurate to seven significant figures.)

1. What frequency does the blood receive?
2. What frequency returns to the source?
3. What beat frequency is produced if the source and returning frequencies are mixed?

Strategy

The first two questions can be answered using ${f}_{\text{obs}}={f}_{s}\left(\frac{{v}_{w}}{{v}_{w}\phantom{\rule{0.25em}{0ex}}±\phantom{\rule{0.25em}{0ex}}{v}_{s}}\right)$ and ${f}_{\text{obs}}={f}_{s}\left(\frac{{v}_{w}\phantom{\rule{0.25em}{0ex}}±\phantom{\rule{0.25em}{0ex}}{v}_{\text{obs}}}{{v}_{w}}\right)$ for the Doppler shift. The last question asks for beat frequency, which is the difference between the original and returning frequencies.

Solution for (a)

(1) Identify knowns:

• The blood is a moving observer, and so the frequency it receives is given by
${f}_{\text{obs}}={f}_{s}\left(\frac{{v}_{w}±{v}_{\text{obs}}}{{v}_{w}}\right).$
• ${v}_{b}$ is the blood velocity ( ${v}_{\text{obs}}$ here) and the plus sign is chosen because the motion is toward the source.

(2) Enter the given values into the equation.

${f}_{\text{obs}}=\left(2,\text{500},\text{000 Hz}\right)\left(\frac{\text{1540 m/s}+0\text{.}\text{2 m/s}}{\text{1540 m/s}}\right)$

(3) Calculate to find the frequency: 20,500,325 Hz.

Solution for (b)

(1) Identify knowns:

• The blood acts as a moving source.
• The microphone acts as a stationary observer.
• The frequency leaving the blood is 2,500,325 Hz, but it is shifted upward as given by
${f}_{\text{obs}}={f}_{s}\left(\frac{{v}_{w}}{{v}_{w}\phantom{\rule{0.25em}{0ex}}–\phantom{\rule{0.25em}{0ex}}{v}_{b}}\right).$

${f}_{obs}$ is the frequency received by the speaker-microphone.

• The source velocity is ${v}_{b}$ .
• The minus sign is used because the motion is toward the observer.

The minus sign is used because the motion is toward the observer.

(2) Enter the given values into the equation:

${f}_{\text{obs}}=\left(2,\text{500},\text{325 Hz}\right)\left(\frac{\text{1540 m/s}}{\text{1540 m/s}-0\text{.}\text{200 m/s}}\right)$

(3) Calculate to find the frequency returning to the source: 2,500,649 Hz.

Solution for (c)

(1) Identify knowns:

• The beat frequency is simply the absolute value of the difference between ${f}_{s}$ and ${f}_{\text{obs}}$ , as stated in:
${f}_{B}=\mid {f}_{\text{obs}}-{f}_{s}\mid .$

(2) Substitute known values:

$\mid 2,\text{500},\text{649}\phantom{\rule{0.25em}{0ex}}\text{Hz}-2,\text{500},\text{000}\phantom{\rule{0.25em}{0ex}}\text{Hz}\mid$

(3) Calculate to find the beat frequency: 649 Hz.

Discussion

The Doppler shifts are quite small compared with the original frequency of 2.50 MHz. It is far easier to measure the beat frequency than it is to measure the echo frequency with an accuracy great enough to see shifts of a few hundred hertz out of a couple of megahertz. Furthermore, variations in the source frequency do not greatly affect the beat frequency, because both ${f}_{s}$ and ${f}_{\text{obs}}$ would increase or decrease. Those changes subtract out in ${f}_{B}=\mid {f}_{\text{obs}}-{f}_{s}\mid .$

Calculate the work done by an 85.0-kg man who pushes a crate 4.00 m up along a ramp that makes an angle of 20.0º20.0º with the horizontal. (See [link] .) He exerts a force of 500 N on the crate parallel to the ramp and moves at a constant speed. Be certain to include the work he does on the crate an
What is thermal heat all about
why uniform circular motion is called a periodic motion?.
when a train start from A & it returns at same station A . what is its acceleration?
what is distance of A to B of the stations and what is the time taken to reach B from A
BELLO
the information provided is not enough
aliyu
Hmmmm maybe the question is logical
yusuf
where are the parameters for calculation
HENRY
there is enough information to calculate an AVERAGE acceleration
Kwok
mistake, there is enough information to calculate an average velocity
Kwok
~\
Abel
what is the unit of momentum
Abel
wha are the types of radioactivity ?
what are the types of radioactivity
Worku
what is static friction
It is the opposite of kinetic friction
Mark
static fiction is friction between two surfaces in contact an none of sliding over on another, while Kinetic friction is friction between sliding surfaces in contact.
MINDERIUM
I don't get it,if it's static then there will be no friction.
author
It means that static friction is that friction that most be overcome before a body can move
kingsley
static friction is a force that keeps an object from moving, and it's the opposite of kinetic friction.
author
It is a force a body must overcome in order for the body to move.
Eboh
If a particle accelerator explodes what happens
Eboh
why we see the edge effect in case of the field lines of capacitor?
Arnab
what is wave
what is force
Muhammed
force is something which is responsible for the object to change its position
MINDERIUM
more technically it is the product of mass of an object and Acceleration produced in it
MINDERIUM
wave is disturbance in any medium
iqra
energy is distributed in any medium through particles of medium.
iqra
If a particle accelerator explodes what happens
we have to first figure out .... wats a particle accelerator first
Teh
What is surface tension
The resistive force of surface.
iqra
Who can tutor me on simple harmonic motion
on both a string and peldulum?
Anya
spring*
Anya
Yea
yusuf
Do you have a chit-chat contact
yusuf
I dont have social media but i do have an email?
Anya
Which is
yusuf
Where are you chatting from
yusuf
I don't understand the basics of this group
Jimmy
teach him SHM init
Anya
Simple harmonic motion
yusuf
how.an.equipotential.line is two dimension and equipotential surface is three dimension ?
definition of mass of conversion
Force equals mass time acceleration. Weight is a force and it can replace force in the equation. The acceleration would be gravity, which is an acceleration. To change from weight to mass divide by gravity (9.8 m/s^2).
Marisa
how many subject is in physics
the write question should be " How many Topics are in O- Level Physics, or other branches of physics.
effiom
how many topic are in physics
Praise
Praise what level are you
yusuf
If u are doing a levels in your first year you do AS topics therefore you do 5 big topic i.e particles radiation, waves and optics, mechanics,materials, electricity. After that you do A level topics like Specific Harmonic motion circular motion astrophysics depends really
Anya
Yeah basics of physics prin8
yusuf
Heat nd Co for a level
yusuf
yh I need someone to explain something im tryna solve . I'll send the question if u down for it
a ripple tank experiment a vibrating plane is used to generate wrinkles in the water .if the distance between two successive point is 3.5cm and the wave travel a distance of 31.5cm find the frequency of the vibration
Tamdy
hallow
Boniface
Boniface
the range of objects and phenomena studied in physics is
Boniface