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)
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%.
de Broglie wavelength
is given by
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
is the velocity of the particle, EK
is the kinetic energy, and V
is the potential difference that can accelerate a charged particle.
, is the probability of a radioactive decay per unit time.
at t=t1/2, N=N0/2: after one half-life the number of nuclei halves
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
We can find a value for
decimal to binary conversion
can be completed by dividing by 2 and keeping track of the remainder: an example is 21
which gives 10101.
is transformed energy which is no longer available to perform useful work. (d)
are not fundamental but can be expressed in terms of fundamental units.
occurs when two waves meet such that the resultant wave displacement is less than that of the individual waves: path difference or phase difference .
is the linear distance of the position of an object from a given reference point. (d.)
is the apparent change in the frequency of a wave source due to the relative motion between the wave source and observer.
Let = observed frequency
= actual wave frequency
= speed/velocity of waves in medium (fixed by medium and its properties)
= speed/velocity of wave source
= speed/velocity of observer
For a moving source - stationary observer
(change in observed wavelength of source)
Use , (decrease in wavelength), if wave source moves towards observer
Use , (increase in wavelength), if wave source moves away from observer
For a moving observer - stationary source
(change in relative speed of waves)
Use , , increase in relative speed/velocity of waves (), if observer moves towards wave source.
Use , , decrease in relative speed/velocity of waves (), if observer moves away from wave source.
For electromagnetic waves
where v is the speed of the wave source and c is the speed of electromagnetic waves in a vacuum.