OCR · A-Level · Physics
Course version: H556 · Version from Sept 2015
(e) reflection of ultrasound at a boundary; Iᵣ/I₀ = (Z₂ − Z₁)²/(Z₂ + Z₁)²
Full specification wording
Using ultrasound: (e) reflection of ultrasound at a boundary; Iᵣ/I₀ = (Z₂ − Z₁)²/(Z₂ + Z₁)²
When ultrasound meets a boundary between two media, part of the wave is reflected and part is transmitted.
Checked against the OCR H556 specification (opens in a new tab) on .
- Point 5 of 8
- 4 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
When ultrasound meets a boundary between two media, part of the wave is reflected and part is transmitted. The reflected fraction depends on the acoustic impedances Z₁ and Z₂ of the two media. The intensity reflection coefficient is Iᵣ/I₀ = (Z₂ − Z₁)²/(Z₂ + Z₁)². Here I₀ is the incident intensity and Iᵣ is the reflected intensity. If Z₁ = Z₂, the numerator is zero, so no reflection occurs. A large impedance mismatch gives strong reflection. For example, at a soft-tissue–air boundary, Z₂ is much smaller than Z₁, so the fraction reflected is close to 1. This is why a coupling gel is needed in scanning.
What earns the marks
- State that the intensity reflection coefficient gives the fraction of incident intensity reflected at a boundary.
- Use the equation Iᵣ/I₀ = (Z₂ − Z₁)²/(Z₂ + Z₁)² correctly, squaring the difference and the sum.
- Recognise that reflection is zero when the two acoustic impedances are equal.
- Recognise that reflection is large when the impedance mismatch is large.
- Relate strong reflection at a soft-tissue–air boundary to the need for coupling gel.
Common mistakes and how to put them right
Forgetting to square the numerator and denominator.
Put it right: The correct form has both squared.
Mixing up Z₁ and Z₂.
Put it right: The equation is symmetric in Z₁ and Z₂, so the order does not change the result, but substituting the wrong values does.
Assuming that a large impedance difference gives a small reflected fraction.
Put it right: In fact a large difference gives a reflected fraction close to 1.
Using the equation for amplitude reflection rather than intensity reflection.
Put it right: The intensity ratio involves the square of the impedance difference over the sum.
Exam tips
- Check whether the question asks for a ratio, a percentage or a fraction; convert carefully if needed.
- If one impedance is much larger than the other, the ratio approaches 1; use this to sanity-check your answer.
- Remember that the equation is symmetric: swapping Z₁ and Z₂ gives the same result.
- In multiple-choice questions, eliminate options that are greater than 1 or negative, since a fraction of intensity reflected cannot be outside 0 to 1.
Try the lesson
The start of the Using ultrasound: (e) reflection of ultrasound at a boundary; Iᵣ/I₀ = (Z₂ − Z₁)²/(Z₂ + Z₁)² lesson, made from checked teaching notes for this specification point.
Listen
When ultrasound meets a boundary between two media, part of the wave is reflected and part is transmitted. The reflected fraction depends on the acoustic impedances Z₁ and Z₂ of the two media. The intensity reflection coefficient is Iᵣ/I₀ = (Z₂ − Z₁)²/(Z₂ + Z₁)². Here I₀ is the incident intensity and Iᵣ is the reflected intensity. If Z₁ = Z₂, the numerator is zero, so no reflection occurs. A large impedance mismatch gives strong reflection. For example, at a soft-tissue–air boundary, Z₂ is much smaller than Z₁, so the fraction reflected is close to 1. This is why a coupling gel is needed in scanning. A strong answer earns marks for these points. State that the intensity reflection coefficient gives the fraction of incident intensity reflected at a boundary. Use the equation Iᵣ/I₀ = (Z₂ − Z₁)²/(Z₂ + Z₁)² correctly, squaring the difference and the sum. Recognise that reflection is zero when the two acoustic impedances are equal. Recognise that reflection is large when the impedance mismatch is large. Exam tip: Check whether the question asks for a ratio, a percentage or a fraction; convert carefully if needed.
Key words
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Intensity reflection coefficient
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Acoustic impedance mismatch
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Reflection and transmission of ultrasound at boundaries
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Coupling gel
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See every definition
- Intensity reflection coefficient
- The fraction of incident intensity reflected at a boundary, given by Iᵣ/I₀ = (Z₂ − Z₁)²/(Z₂ + Z₁)², where I₀ is the incident intensity and Iᵣ is the reflected intensity.
- Acoustic impedance mismatch
- A difference between the acoustic impedances Z₁ and Z₂ of two media; a large mismatch gives strong reflection, and if Z₁ = Z₂ the numerator is zero so no reflection occurs.
- Reflection and transmission of ultrasound at boundaries
- When ultrasound meets a boundary between two media, part of the wave is reflected and part is transmitted, with the reflected fraction depending on the acoustic impedances of the two media.
- Coupling gel
- Needed in scanning because at a soft-tissue–air boundary Z₂ is much smaller than Z₁, so the fraction reflected is close to 1; the gel improves transmission.
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