All subjects · Physics · WPH12 (Unit 2)

Intensity, reflection and pulse-echo techniques

Waves carry energy, measured by intensity. When they meet a boundary, some energy reflects, which is the basis of ultrasound scanning, sonar and radar.

Intensity

Intensity is the power per unit area at right angles to the direction of travel: I = P / A, measured in W/m². For a source radiating equally in all directions, the power spreads over a sphere of area 4πr², so intensity falls with distance.

Reflection and transmission

When a wave reaches a boundary between two media, it is partly reflected and partly transmitted. How much is reflected depends on how different the two media are. Ultrasound reflects at boundaries between tissues; light partly reflects from a glass window.

Pulse-echo

A short pulse is sent out and the time t until its echo returns is measured. The wave travels there and back, so the distance to the reflector is d = vt / 2.

Limits on the information

Wavelength: a wave cannot show detail much smaller than its wavelength. Higher frequency means shorter wavelength and finer detail.
Pulse duration: a long pulse means echoes from boundaries close together overlap and cannot be told apart. Short pulses give better depth resolution.

Worked example

Ultrasound travels at 1540 m/s in soft tissue. An echo returns 65 μs after the pulse is sent. How deep is the boundary?

d = vt / 2
= 1540 x 65 x 10^-6 / 2 = 0.050 m

Answer: The boundary is 5.0 cm deep.

Key idea: I = P/A. At a boundary a wave is partly reflected, partly transmitted. Pulse-echo: d = vt/2; detail limited by wavelength and pulse length.

Check yourself

A 2.0 W laser beam has a cross-sectional area of 4.0 x 10^-6 m². Find its intensity in kW/m².
Show answer
500 kW/m². I = P / A = 2.0 / 4.0 x 10^-6 = 5.0 x 10⁵ W/m² = 500 kW/m².
Sunlight of intensity 1.0 kW/m² falls on a solar panel of area 1.6 m². Find the power received in W.
Show answer
1600 W. P = IA = 1000 x 1.6 = 1600 W.
A 60 W source radiates equally in all directions. Find the intensity 2.0 m away, in W/m², to 3 s.f.
Show answer
1.19 W/m². I = P / 4πr² = 60 / (4π x 4.0) = 1.19 W/m².
A sonar pulse returns from the sea bed 0.80 s after it is sent. Sound travels at 1500 m/s in sea water. Find the depth in m.
Show answer
600 m. d = vt / 2 = 1500 x 0.80 / 2 = 600 m.
Why is the distance to a reflector vt/2 rather than vt?
- Half the wave is absorbed
- The speed halves after reflection
- The pulse travels to the reflector and back
- Only half the pulse is reflected
Show answer
The pulse travels to the reflector and back. The time measured is for the round trip.
Why does a higher ultrasound frequency show finer detail?
- It has a shorter wavelength
- It travels faster
- It is reflected less
- It has a longer pulse
Show answer
It has a shorter wavelength. Detail smaller than about one wavelength cannot be resolved, and λ = v/f.
Why must pulses in a pulse-echo system be short?
- So the pulses travel faster
- So the frequency is lower
- So echoes from boundaries close together do not overlap
- So less energy is reflected
Show answer
So echoes from boundaries close together do not overlap. Long pulses blur echoes from nearby boundaries together.
What happens to a wave when it reaches a boundary between two different media?
- It is always completely reflected
- It is always completely absorbed
- It passes through unchanged
- It is partly reflected and partly transmitted
Show answer
It is partly reflected and partly transmitted. Some energy reflects and some carries on into the second medium.

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Last updated 7 November 2026. Spotted a mistake? Tell us.