Cambridge International AS & A Level · 24 · structured
How ultrasound is produced, reflected and located
How ultrasound is produced, reflected and located · Original GioPhysics question with a detailed, mark-by-mark answer guide.
- Demand
- demanding
- Marks
- 11
- Topics
- 5
- Answer
- Complete
An ultrasound transducer sends short pulses into a uniform medium with density 1000 kg m⁻³ and sound speed 1500 m s⁻¹. A boundary with a second medium of acoustic impedance 2.00×10⁶ kg m⁻² s⁻¹ returns an echo 80.0 μs after transmission. Assume normal incidence.
- (a)
State both directions of the piezoelectric effect and explain how a transducer uses them to generate and detect ultrasound pulses.
4 marks - (b)
Explain how the echo provides information about an internal boundary and calculate its depth.
3 marks - (c)
Define specific acoustic impedance, calculate it for the first medium, and find the fraction of incident intensity reflected at the boundary.
4 marks
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(a)
State both directions of the piezoelectric effect and explain how a transducer uses them to generate and detect ultrasound pulses.
Identify what the question is testing, organise the response into distinct mark-earning points, and make every conclusion traceable to a physical principle or to the evidence supplied.
- 1
Applying a p.d. across a suitable crystal changes its shape.
- 2
Mechanical deformation of that crystal generates an e.m.f.
- 3
An alternating p.d. causes vibrations that launch ultrasound; a short drive pulse and damping produce a brief sound pulse.
- 4
Returning ultrasound changes pressure on/deforms the crystal, producing a voltage signal for detection.
(b)
Explain how the echo provides information about an internal boundary and calculate its depth.
List the given quantities with units, identify the required quantity, write the governing relationship before substituting, and keep extra digits until the final line so rounding does not distort the result.
- 1
A boundary between media with different acoustic impedances partly reflects the pulse.
- 2
The measured time is an outward-and-return journey, so distance to the boundary is ct/2.
- 3
d=1500×80.0×10⁻⁶/2=0.0600 m, or 6.00 cm; multiple echo times locate multiple boundaries.
(c)
Define specific acoustic impedance, calculate it for the first medium, and find the fraction of incident intensity reflected at the boundary.
List the given quantities with units, identify the required quantity, write the governing relationship before substituting, and keep extra digits until the final line so rounding does not distort the result.
- 1
Specific acoustic impedance is density multiplied by sound speed in the medium: Z=ρc.
- 2
Z₁=1000×1500=1.50×10⁶ kg m⁻² s⁻¹.
- 3
Use I_R/I_inc=[(Z₂−Z₁)/(Z₂+Z₁)]².
- 4
The fraction is (0.50/3.50)²=0.0204, or about 2.04%.
Complete marking guidance
Use these worked steps alongside the part-by-part answers. They explain the method and mark allocation; they do not add extra marks.
- (a) Applying a p.d. across a suitable crystal changes its shape.
- (a) Mechanical deformation of that crystal generates an e.m.f.
- (a) An alternating p.d. causes vibrations that launch ultrasound; a short drive pulse and damping produce a brief sound pulse.
- (a) Returning ultrasound changes pressure on/deforms the crystal, producing a voltage signal for detection.
- (b) A boundary between media with different acoustic impedances partly reflects the pulse.
- (b) The measured time is an outward-and-return journey, so distance to the boundary is ct/2.
- (b) d=1500×80.0×10⁻⁶/2=0.0600 m, or 6.00 cm; multiple echo times locate multiple boundaries.
- (c) Specific acoustic impedance is density multiplied by sound speed in the medium: Z=ρc.
- (c) Z₁=1000×1500=1.50×10⁶ kg m⁻² s⁻¹.
- (c) Use I_R/I_inc=[(Z₂−Z₁)/(Z₂+Z₁)]².
- (c) The fraction is (0.50/3.50)²=0.0204, or about 2.04%.
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