Home » 國際課程 » A-level課程 » Details

CIE A Level Physics復(fù)習(xí)筆記24.1.5 Attenuation of Ultrasound in Matter

Category: A-level課程, 教材筆記, 福利干貨 Date: 2022年8月17日下午3:47

Attenuation of Ultrasound in Matter

Attenuation of ultrasound is defined as:

The reduction of energy due to the absorption of ultrasound as it travels through a material

The attenuation coefficient of the ultrasound is expressed in?decibels per centimetre?lost for every incremental increase in megahertz frequency
- Generally, 0.5 dB/cm is lost for every 1MHz
The intensity I of the ultrasound decreases with distance?x, according to the equation:

I = I₀?e^?μx

Where:
- I₀?= the intensity of the incident beam (W m^-2)
- I?= the intensity of the reflected beam (W m^-2)
- μ = the absorption coefficient (m^-1)
- x?= distance travelled through the material (m)
The absorption coefficient μ, will vary from material to material
Attenuation is not a major problem in ultrasound scanning as the scan relies on the reflection of the ultrasounds at boundaries of materials

Attenuation of Ultrasound Graph, downloadable AS & A Level Physics revision notes

When the intensity is expressed in decibels, the amplitudes of the echoes can be seen to decrease linearly

Worked Example

The thickness x of the layer of fat on an animal, as shown in the diagram, is to be investigated using ultrasound. WE - Attenuation of Ultrasound question image, downloadable AS & A Level Physics revision notes

The intensity of the parallel ultrasound beam entering the surface S of the layer of fat is I.

The beam is reflected from the boundary between fat and muscle.

The intensity of the reflected ultrasound detected at the surface S of the fat is 0.012I.Using the table below, calculate:a) The intensity reflection coefficient at the boundary between the fat and the muscle.b) The thickness x of the layer of fat. WE - Attenuation of Ultrasound table, downloadable AS & A Level Physics revision notes

Part (a)

Step 1: ??????????

Write down the equation for intensity reflection coefficient α

Intensity Reflection Coefficient Worked Example equation 1

Step 2: ??????????

Calculate the intensity reflection coefficient

Attenuation of Ultrasound in Matter Worked Example equation 2

This means that 0.018 of the intensity is reflected at the interface between fat and muscle. This reflected intensity will move back through the fat towards surface S.

Part (b)

Step 1: ??????????

Write out the known quantities

The intensity of the ultrasound pulse is affected 3 times:

1. Attenuation from the surface S to the fat-muscle boundary
2. Reflection at the boundary
3. Attenuation from the boundary back to the surface S

After being transmitted in the fat, the intensity at surface S is given to be 0.012 I.

Therefore, the intensity is 0.018 I at the fat-muscle boundary, and as the ultrasound moves through the fat, it gets attenuated and the new intensity at the surface S is now 0.012 I

Incident intensity, equal to the intensity of the reflected pulse, I₀?= 0.018 I × e^?μx

Transmitted intensity, I = 0.012 I

Absorption coefficient, μ = 48 m^-1

Thickness of fat = x

Step 2: ??????????

Write out the equation for attenuation

I = I₀?e^?μx

Step 3: ??????????

Substitute in values for intensity and simplify

0.012 I = [0.018 I × e^?μx] × e^?μx

0.012 = 0.018 e^?2μx

Step 4: ??????????