Reflection, transmission and pulse-echo techniquesEdexcel International A Level Physics: Revision notes

When a wave meets the boundary (interface) between two media, some of it is reflected and some is transmitted into the second medium. The frequency of the wave stays the same.

• The more different the two media are, the more energy is reflected.
• Some energy is also absorbed in each medium, so echoes are weaker than the emitted wave.
• Reflections at several boundaries give a series of echoes from different depths.

A pulse-echo system sends a short pulse into a medium and detects the echo reflected from a boundary. It is used in medical ultrasound scans, ship echo sounders, sonar and radar.

Short pulses are used because the same device emits and detects, so echoes can be received in the gaps between pulses.

In medical scans a gel is spread on the skin. This removes air, which would otherwise reflect nearly all the ultrasound at the skin surface.

The pulse travels to the boundary and back, so the distance travelled is twice the depth:

$d = \frac{vt}{2}$

where $v$ is the speed of the wave in the medium and $t$ is the time between emission and detection.

Worked example. An echo sounder in seawater ($v = 1.5 \times 10^3$ m s⁻¹) detects an echo after 0.080 s. Distance = 1.5 × 10³ × 0.080 = 120 m, so the depth is 60 m.

Waves cannot resolve detail much smaller than their wavelength, because they diffract round it instead of reflecting. To see smaller objects, use a shorter wavelength (a higher frequency), since $\lambda = v/f$.

Example. Ultrasound of 2.5 MHz in tissue ($v = 1540$ m s⁻¹) has λ = 6.2 × 10⁻⁴ m, so a 0.30 mm structure is not resolved. At 10 MHz, λ = 1.5 × 10⁻⁴ m, and it would be.

If a pulse lasts longer than the time between two echoes, the echoes overlap and look like one. Two boundaries a distance $s$ apart give echoes separated by $t = 2s/v$.

Example. Two surfaces 5.0 mm apart in steel ($v = 5900$ m s⁻¹): t = 2 × 5.0 × 10⁻³ / 5900 = 1.7 × 10⁻⁶ s. A 4.0 μs pulse is too long to separate them; pulses shorter than 1.7 μs are needed.