IB Physics Glossary

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U

Ultrasound A-scan

is an amplitude-modulated scan with information represented as a graph of signal strength against time.

Ultrasound B-scan

is a brightness-modulated scan with information represented as levels of brightness.

Ultrasound choice of frequency

is selected based on
  1. the resolution or size of smallest object being scanned
  2. attenuation which increases with frequency
  3. pulse length.
The best choice of frequency occurs when the organ/object being imaged is about 200 wavelengths from the ultrasound probe:
$$f = 200 \lambda = 200 \frac{c} {d}$$
where c is the speed of sound waves in tissue and d is the depth of the organ/object.

Uncertainties

    •    resulting from measurements are combined under the following rules:

addition/subtraction of quantities => add absolute errors

If $$y = a \pm b \pm c $$, then $$\Delta y = \pm (\Delta a + \Delta b+ \Delta c)$$.


multiplication/division of quantities = add relative/fractional/percentage errors

If $$y = a \times b \times c$$, then

$$\frac{\Delta y}{y} = \pm (\frac{\Delta a}{a} + \frac{\Delta b}{b} + \frac{\Delta c}{c})$$, or, $$\Delta y(\%)= \pm (\Delta a(\%) + \Delta b(\%) + \Delta c(\%))$$
and
$${\Delta y} = \pm y \times (\frac{\Delta a}{a} + \frac{\Delta b}{b} + \frac{\Delta c}{c})$$, or, $$\Delta y= \pm y \times (\Delta a(\%) + \Delta b(\%) + \Delta c(\%))$$.


If $$y = a \div b \div c$$, then 

$$\frac{\Delta y}{y} = \pm (\frac{\Delta a}{a} + \frac{\Delta b}{b} + \frac{\Delta c}{c})$$, or, $$\Delta y(\%)= \pm (\Delta a(\%) + \Delta b(\%) + \Delta c(\%))$$
and 
$${\Delta y} = \pm y \times (\frac{\Delta a}{a} + \frac{\Delta b}{b} + \frac{\Delta c}{c})$$, or, $$\Delta y= \pm y \times (\Delta a(\%) + \Delta b(\%) + \Delta c(\%))$$.

raising quantity to n'th power = multiply relative/fractional/percentage error by n

If $$y = a^n$$, then
$$\frac{\Delta y}{y} = \pm |n| \times \frac{\Delta a}{a}$$, or, $$\Delta y(\%)= \pm |n| \times \Delta a(\%)$$
and 
$${\Delta y} = \pm y \times |n| \times \frac{\Delta a}{a}$$, or, $$\Delta y= \pm y \times |n| \times \Delta a(\%)$$.

Unified atomic mass unit (u)

is 1/12th the mass of a neutral carbon-12 atom.

Uniform acceleration

occurs when the acceleration $$a$$ is held constant.
Since acceleration is a vector quantity, constant implies a uniform magnitude and direction for the acceleration. The equations of uniform acceleration are

$$v=u + at$$ (not given on IB Physics Data Booklet)

$$s = \frac{u+v}{2} t$$

$$s=ut + \frac{1}{2} a t^2$$

$$v^2=u^2 + 2 as$$

where u is the initial velocity, v is the final velocity after time t, a is the acceleration and s is the displacement.