Ultrasound and Its Applications

Ultrasound is sound with a frequency above 20 000 Hz (20 kHz), beyond the upper limit of human hearing. It has the same properties as audible sound (longitudinal, needs a medium, reflects at boundaries) but its high frequency gives it useful properties.

Medical imaging (ultrasound scanning)

1. A transducer on the skin surface emits short pulses of ultrasound into the body.
2. At each boundary between different tissues (e.g. muscle-bone, fluid-organ), some ultrasound is reflected back.
3. The transducer detects the reflected pulses.
4. The time delay and intensity of each reflection are processed by a computer to build an image.

Advantages over X-rays:

• No ionising radiation, so safe for pregnant women and repeated scans.
• Can image soft tissues that X-rays pass through.
• Real-time imaging (moving images of a fetus, blood flow).

Industrial testing

Ultrasound detects internal cracks or flaws in metal. A pulse is sent through the material. If there is a crack, some ultrasound reflects from the crack boundary before reaching the back wall. The early reflection shows up on the display.

Distance calculation

When ultrasound is reflected, the pulse travels to the boundary and back. The distance to the boundary is:

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

where $v$ is the speed of ultrasound in the material and $t$ is the total time for the pulse to travel there and back. The factor of 2 accounts for the round trip.

Worked example

An ultrasound pulse takes 0.00012 s to travel to a boundary and return. The speed of ultrasound in the tissue is 1540 m/s. Calculate the depth of the boundary.

$d = \frac{1540 \times 0.00012}{2} = \frac{0.185}{2} = 0.092\text{ m} = 9.2\text{ cm}$

Common errors and how to correct them

Forgetting to divide by 2. The pulse travels to the boundary and back, so the total distance is twice the depth. The depth is $vt/2$, not $vt$.

Confusing ultrasound with electromagnetic waves. Ultrasound is a mechanical (longitudinal) wave. It needs a medium and does not travel through a vacuum.

How to apply this in an exam

State that ultrasound is reflected at boundaries between materials of different density. Use $d = vt/2$ for distance calculations. When comparing with X-rays, focus on the safety advantage (no ionising radiation) and the ability to image soft tissue.