IB Physics Glossary



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D

Damping

involves a force that is always in the opposite direction to the direction of motion of the oscillating particle/system and the force is a dissapative force which reduces the total energy of the system. (d)


damping


Also

\frac{E_{n+1}}{E_n}=\(\frac{A_{n+1}}{A_n}\)^2

the ratio of successive peak energies equals the ratio of successive amplitudes squared. For example, in the case below, the amplitude falls from 4.3 cm to 2.7 cm. Remaining energy is (2.7/4.3)2 = 0.394 or 39.4%.

damping_2

de Broglie wavelength

is given by
\lambda = \frac{h}{p}.

where h is Planck's constant, and p is the momentum of a particle.

Since waves behave like particles, de Broglie suggested particles can behave like waves with wavelength λ.

The formula, since p = m v, and EK = p2/2m, can be written as

\lambda = \frac{h}{p}=\frac{h}{mv}=\frac{h}{\sqrt{2mE_K}}=\frac{h}{\sqrt{2 m e V}},

where v is the velocity of the particle, EK is the kinetic energy, and V is the potential difference that can accelerate a charged particle.

Decay constant

\lambda, is the probability of a radioactive decay per unit time.

N=N_0e^{-\lambda t}
at t=t1/2, N=N0/2: after one half-life the number of nuclei halves
=>
\frac{N_0}{2}=N_0e^{\lambda t_{1/2}}
=>
\frac{1}{2}=e^{-\lambda t_{1/2}}
or
 2=e^{\lambda t_{\frac{1}{2}}}
=>
\ln 2=\lambda t_{1/2}
or
t_{1/2} = \frac{\ln 2}{\lambda}.

A shorter half-life indicates a more active sample or a higher value for the decay constant (greater probability for a decay).

A a short half-life sample can be measured from the activity-time graph, simply finding the time for the activity to fall by a factor of 2.

For a long half-life sample, the activity, A, is measured at the same time as the mass, m, of the sample. We know 
number of atoms, N = number of moles, n, times Avogadro's constant, NA
and number of moles, n = mass in grams, m/atomic mass number, a, therefore

N = \frac{m}{a} \times N_A

Since 

A = \lambda N then \lambda = \frac{A}{N}

We can find a value for \lambda and t_{1/2}.

decimal to binary conversion

can be completed by dividing by 2 and keeping track of the remainder: an example is 21

remainder 

21
1 (lsb)10
05
12
01
1 (msb)0

which gives 10101.


Degraded energy

is transformed energy which is no longer available to perform useful work. (d)

Derived units

are not fundamental but can be expressed in terms of fundamental units.

Destructive interference

occurs when two waves meet such that the resultant wave displacement is less than that of the individual waves: path difference = (n+ \frac{1}{2}) \times \lambda or phase difference = (2n + 1) \times \pi.

Displacement

is the linear distance of the position of an object from a given reference point. (d.)
s=\Delta x=x_2-x_1.

Doppler effect

is the apparent change in the frequency of a wave source due to the relative motion between the wave source and observer.

Let f^\prime = observed frequency
f = actual wave frequency
v = speed/velocity of waves in medium (fixed by medium and its properties)
u_s = speed/velocity of wave source
u_0 = speed/velocity of observer

For a moving source - stationary observer
(change in observed wavelength of source)

f^\prime = f \left(\frac{v}{v\pm u_s}\right)

Use \pm \rightarrow -, f^\prime > f, \lambda^\prime < \lambda (decrease in wavelength), if wave source moves towards observer

Use \pm \rightarrow +, f^\prime < f, \lambda^\prime > \lambda (increase in wavelength), if wave source moves away from observer


For a moving observer - stationary source
(change in relative speed of waves)

f^\prime = f \left(\frac{v \pm u_0}{v}\right)

Use \pm \rightarrow +, f^\prime > f, increase in relative speed/velocity of waves (v + u_0), if observer moves towards wave source.

Use \pm \rightarrow -, f^\prime < f, decrease in relative speed/velocity of waves (v - u_0), if observer moves away from wave source.

For electromagnetic waves

\Delta f = \frac{v}{c} f

where v is the speed of the wave source and c is the speed of electromagnetic waves in a vacuum.

Doppler flow-speed measurements

can be used to determine the speed of moving objects such as that of
  • a car with a speed "gun"
  • blood flow with ultrasound
through

U = v \frac{|f^\prime - f|}{f^\prime + f} = v \frac{f^-}{f^+}

where
f^\prime= measured/shifted frequency
f = actual wave frequency
f^+ = f^\prime + f
f^- = f^\prime - f
v= speed/velocity of waves in medium (fixed by medium and its properties)
U= speed/velocity of moving target source.

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