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Ultrasound

Key idea: O Level ultrasound: define ultrasound, use echo timing d = vt/2, and explain applications in medical scanning and sonar.

  • SEC G3 Physics 2027
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Learning objectives

  • Describe wave generation by vibrating sources, ropes and springs
  • Describe ripple-tank waves using wavefronts
  • Explain that waves transfer energy
  • Explain that wave energy transfer does not transfer matter
  • Use amplitude, frequency and wavelength to describe wave motion
  • Define and use wave speed and period and interpret wave graphs
  • Recall and apply wave speed = frequency × wavelength
  • Compare transverse and longitudinal waves and give examples
  • Explain sound production by vibration and the need for a medium
  • Describe sound using compressions and rarefactions
  • Relate sound loudness to amplitude and pitch to frequency
  • Explain reflected-sound echoes and use them to measure distance
  • Explain ultrasound use in sonar and soft-tissue scanning
  • Use the normal, angle of incidence and angle of reflection
  • Apply the law of reflection in constructions, measurements and calculations
  • Use the normal, angle of incidence and angle of refraction
  • Apply sin i divided by sin r as a constant for a fixed pair of media
  • Define refractive index as vacuum light speed divided by medium light speed
  • Explain the critical angle
  • Explain the conditions for total internal reflection
  • Apply total internal reflection to optical fibres and state advantages
  • Describe how a thin converging lens acts on a light beam
  • Define the focal length of a converging lens
  • Construct real and virtual image ray diagrams for a thin converging lens
  • Describe lens images as real or virtual, magnified or diminished, and upright or inverted

1. Definition

A. Ultrasound

Ultrasound is sound with frequency greater than 20 000 Hz (20 kHz).

2. Key Ideas

  • Ultrasound is a sound wave (mechanical, needs a medium) but with very high frequency.
  • Ultrasound is used for echo methods: send a pulse, detect the echo, and use the time taken to find distance.
  • Higher frequency → shorter wavelength → can give better detail (useful for imaging).

3. Detailed Explanations

A. Sonar (echo sounding)

  1. A transmitter sends out a short ultrasound pulse.
  2. The pulse reflects from an object (e.g. seabed, a shoal of fish).
  3. A receiver detects the echo after time t.

Because the pulse travels to the object and back, the one-way distance is:

d = vt/2

Ultrasound pulse and echo pathAn ultrasound pulse travels from transducer to reflector and back. Total path is two times the one-way distance.TransducerReflectorOutgoing pulseEcho returnd2d = vt, so d = vt / 2
Pulse path is 2d in time t, so the one-way distance is d = vt/2.

where v is the speed of sound in that medium (e.g. water).

B. Medical scanning (soft tissue)

Ultrasound imaging uses reflections at boundaries between different tissues:

  1. Short ultrasound pulses are sent into the body.
  2. Echoes occur where tissues change (e.g. muscle–fat boundary).
  3. A computer uses the echo times to build an image.
A probe on the skin sends an ultrasound pulse through fat, muscle and an organ. Echoes return from the fat–muscle boundary 2.0 cm deep after about 26 µs and from the muscle–organ boundary 5.0 cm deep after about 65 µs.
Each boundary returns an echo; with v ≈ 1540 m/s in soft tissue, depth = vt ÷ 2. The computer turns many such echo times into an image.

C. Why ultrasound is useful for imaging

  • Short wavelength can detect smaller features (better detail).
  • Pulses give “time-of-flight” information, so distance can be calculated.

4. Common Mistakes

  • Forgetting the factor of 2 in echo questions (round trip).
  • Using the wrong speed value (speed depends on the medium; water is not the same as air).
  • Confusing ultrasound (high frequency sound) with electromagnetic waves (they are different).

5. Exam Tips

  • Use keywords: pulse, echo, reflection, time taken, distance = vt/2.
  • State clearly: “the pulse travels to the object and back”.
  • If asked why ultrasound (not ordinary audible sound) is used for scanning: mention short wavelength → better detail.

6. Worked Examples

Modelled example 1

Depth from echo time

Core

Problem

An ultrasound pulse is sent toward the seabed. The echo returns after 0.80 s. The speed of sound in seawater is 1500 m s⁻¹. Find the depth.
Study the worked solution

  1. Interpret the echo time

    Method

    Use 0.80 s for the downward and upward journey together.

    Reason

    The receiver detects the pulse only after reflection from the seabed.

    Working

    Total path = vt = (1500)(0.80) = 1200 m.

  2. Calculate the depth

    Method

    Halve the total path length.

    Reason

    Depth is the one-way distance to the seabed.

    Working

    d = vt/2 = 1200/2 = 600 m

Guided practice 2

Distance to a foetus boundary

About 5 min

Problem

In a scan, an echo from a boundary returns after 0.10 ms. Take the speed of ultrasound in tissue as 1500 m s⁻¹. Find the depth of that boundary.

Convert time before using the echo equation

Unit: cm

Hints

Hint 1: convert milliseconds
1 ms = 10⁻³ s.
Hint 2: use the round trip
After multiplying v by t, divide by two.
View solution step by step

  1. Convert the time

    Method

    Express the echo delay in seconds.

    Reason

    The speed is given in metres per second.

    Working

    0.10 ms = 1.0 × 10⁻⁴ s

  2. Calculate the boundary depth

    Method

    Use half the distance travelled during the echo delay.

    Reason

    The pulse travels to the boundary and back.

    Working

    d = ((1500)(1.0 × 10⁻⁴))/2 = 0.075 m = 7.5 cm

Common misconception 3

Speed from echo time

Find and correct the mistake

Learner response

An ultrasound pulse returns after 0.10 s from a seabed 75 m deep. A student uses v = 75/0.10 and obtains 750 m s⁻¹. Diagnose the calculation.

Identify the distance travelled during the measured time

Unit: m/s

View solution step by step

  1. Correct the path length

    Method

    Double the seabed depth to obtain 150 m.

    Reason

    The echo time includes both the outward and return journeys.

    Working

    2d = 2(75) = 150 m

  2. Calculate wave speed

    Method

    Divide total path length by echo time.

    Reason

    Speed uses the distance travelled during the measured interval.

    Working

    v = 2d/t = 150/0.10 = 1500 m s⁻¹

Examiner practice 4

Depth from microseconds

4 marks

Examination question

In a scan, an echo returns after 60 μs. Take the speed in tissue as 1500 m s⁻¹. Find the depth of the boundary in centimetres. [4 marks]

Show unit conversion, echo method and final unit

View solution step by step

  1. Convert the delay

    1 mark

    Method

    Convert microseconds to seconds.

    Reason

    The supplied speed uses seconds.

    Working

    60 μs = 6.0 × 10⁻⁵ s

  2. Calculate and convert depth

    3 marks

    Method

    Use d = vt/2 and express the result in centimetres.

    Reason

    The delay is for the round trip to the tissue boundary and back.

    Working

    d = ((1500)(6.0 × 10⁻⁵))/2 = 4.5 × 10⁻² m = 4.5 cm

Challenge 5

Wavelength of ultrasound

Minimal support

Wave-equation transfer

Ultrasound of frequency 2.0 MHz travels in tissue at 1500 m s⁻¹. Find the wavelength in millimetres.

Switch from echo timing to the wave equation

Hints

Hint 1: convert megahertz
1 MHz = 10⁶ Hz.
Hint 2: choose the relevant equation
Use λ = v/f, not the echo-distance equation.
View solution step by step

  1. Convert frequency

    Method

    Express 2.0 MHz in hertz.

    Reason

    The wave speed is in SI units.

    Working

    2.0 MHz = 2.0 × 10⁶ Hz

  2. Calculate wavelength

    Method

    Divide wave speed by frequency and convert metres to millimetres.

    Reason

    One cycle occupies the distance v/f.

    Working

    λ = 1500/(2.0 × 10⁶) = 7.5 × 10⁻⁴ m = 0.75 mm

7. Mind Stretchers

Mind stretcher 1: Detail vs penetrationExtension

Why might a very high frequency ultrasound give better detail but be less useful for imaging deep inside the body?

Show Answer

Higher frequency has shorter wavelength (better detail), but it is absorbed/scattered more strongly in tissue, so it does not penetrate as deeply.

Mind stretcher 2: Why use pulses?Extension

Why do ultrasound scanners use pulses rather than a continuous wave?

Show Answer

Pulses let the scanner measure the time-of-flight for each echo. This allows distances to be calculated and different boundaries to be separated by their echo times.

8. Practice and next step

Explain one sonar and one medical example using pulse, partial reflection, echo time and distance. Then continue to electromagnetic waves, noting that ultrasound is mechanical rather than electromagnetic.

Continue with the next resource in this course.

Course and syllabus information
Course
SEC G3 Physics
Edition
SEC G3 Physics 2027