Ultrasound

Any sound above the range of human hearing is called ultrasound.  The range of human hearing is from 20 Hz to 20 000 Hz, although the upper limit does decrease with age.  Many animals can hear well into the ultrasound range.  When TV remote controllers were first brought in during the early nineteen seventies, they were ultrasonic.  They had the unfortunate effect of making the cat jump up the curtains each time you changed channel.

Ultrasound is widely used in medicine to:

• take pictures of developing foetuses;
• break up kidney stones;
• to look at internal organs;
• to check blood flow.

The flow of blood through the heart can lead to early diagnosis of heart conditions.  The heart itself is an amazing organ.  The size of a fist, it pumps reliably 3 thousand million times in a life time.  It never gets tired, unless the oxygen supply is cut off - a dangerous condition known as a heart attack.

Ultrasonic waves behave just like sound waves in that they:

•  are transverse;
•  obey the wave equation (c = fl);
•  travel through air at 340 m/s;
•  reflect;
•  refract;
•  superpose;
•  form standing waves.

The ultrasonic probe used by the sonographer in examinations looks like this:

The cable carries a power supply when the probe is transmitting, and carries the signals back to the receiver when receiving.  The probe is coupled to the skin  with a coupling gel.

Since ultrasound has a very high frequency, its wavelength is short.  This enables a better resolution of objects below the skin.  Like other waves, ultrasound travels at different speeds in different materials.  The consequences are:

• The time taken for the echo to return depends on the material as well as the distance.

• The wavelength of the ultrasound changes.

• Refraction and reflection take place at the boundary.

It's like seeing a dim reflection of light in glass.  The more similar the materials are, the less the amplitude of the reflected wave.

The sound property of materials is the acoustic impedance, given by:

Z = rv

where:

• Z - acoustic impedance (kg m^-2 s^-1);

• r - density (kg  m^-3)

• v - speed of sound (m/s).

Although the body is 80 % water, there is quite a range of densities of body tissues.  And this is important.

The intensity of the beam is the energy per unit area.  The intensity can be measured for the transmitted beam and the reflected beam.  They are related by:

The reflected beam is picked up by the piezo-electric transducer and generates a signal to be processed by the receiver.  Although this is a gross simplification, we can show the idea on a CRO screen.

We can measure the time taken.  In this case the time take is shown by 6 squares.  If the time base is 1 ms/cm, the time taken is 6 ms.  We can use the equation:

s = vt

to work out the total distance.  Remember that it's an echo, so the distance from the skin to the transducer is half this figure.

The Doppler Effect

You will know the Doppler effect as the falling note of a car or train horn as it approaches, passes, and then goes away from you.

For any object that is moving with a speed much less than that of sound, it can be shown that the change in frequency is given by:

[Df - change in frequency (Hz); f - original frequency (Hz); v - speed of object (m/s); c - speed of sound (m/s)]

Note that in the Salters' Book, the code for speed of object is u and for the speed of sound is v.  It's not the only time they use codes different to other books!  I will use the codes above for consistency.

For this equation:

• Objects moving towards the observer have a positive speed;  moving away from the observer the speed is negative.

• If the object is moving away, the frequency is lower so that Df is negative.  The wavelength will be longer.

• If the object is coming towards the observer, the frequency is higher, so Df will be positive.  The wavelength will be shorter.

The change in the frequency picked up by the receiver is given by:

Df = fem - frec

where:

• Df is the difference in frequency;

• fem is the transmitted frequency;

• frec is the received frequency.

The Doppler equation is true for any kind of wave.  We can rearrange the Doppler effect equation to give:

Df = femv

        c

The equation above is true for a passive observer (for example if you are standing on a station platform when a train goes past).  However if we are dealing with something that is giving out a signal, then the pulse is travelling towards the target, before being bounced back. 

Suppose we sent a SONAR signal at 1500 m/s towards a submarine that was coming directly at us at 5 m/s.  The signal would hit the submarine at 1505 m/s.  It would bounce off the submarine at 1505 m/s.  But the submarine is moving forward at 5 m/s, so it would propel the reflected wave back at us at 1510 m/s.  So the change in speed would be double.  This would squash the waves by double the expected amount.

So the actual change in signal frequency is double that suggested by the relationship above.  So for an active transducer transmitting waves, the relationship becomes:

Df = 2femv

        c

This is called the Double Doppler Shift, and it applies to laser imaging and radar speed traps.

This relationship is true if the object is heading straight for us.  However if it is at an angle, we need to take that into account.

So our relationship becomes:

Df = 2femv cosq

        c