Oscillations Flashcards
Period, frequency, angular frequency, displacement, amplitude, phase difference, simple harmonic motion, energy in s.h.m., damping, resonance, ultrasound
Period of an oscillation
The time taken to complete one oscillation.
Frequency
The number of oscillations per unit time.
f =
f = 1 / T
Displacement
Distance from the equilibrium position.
Amplitude
Maximum displacement.
Simple harmonic motion
Motion in which:
1) acceleration is directly proportional to its displacement from the equilibrium position
and
2) acceleration and displacement are always in opposite directions.
In s.h.m., the acceleration is always directed towards _____________.
the equilibrium position.
Angular frequency
ω = 2πf
ω = 2π / T
Where does maximum speed occur?
At the equilibrium position,
at x = 0
How do you get the equation for kinetic energy in s.h.m.?
Check notes.
Use KE = 1/2mv^2 and velocity in s.h.m. from formulae sheet.
Potential energy in s.h.m.?
Check notes.
Total energy in s.h.m.?
The total energy remains constant throughout (assuming there are no energy losses). Total energy = KE + PE or Total energy = max. KE or Total energy = max. PE
Sketch, on the same axis, the graph of KE, PE and total energy against displacement.
Check notes.
What are free oscillations?
Oscillations where there are no resistive forces acting on the oscillating system.
What is damping?
Damping happens when resistive forces cause the oscillator’s energy to be dissipated. The total energy of the oscillations decreases and the amplitude of oscillation decreases.
What is the effect of light damping?
It causes the amplitude of vibration to decrease gradually.
Check graph in notes.
What is the effect of critical damping?
It causes the displacement to be reduced to zero in the shortest time possible, without any oscillation of the object.
Check graph in notes.
What is the effect of overdamping?
It also causes an exponential reduction in displacement, but over a greater time (compared to critical damping).
Check graph in notes.
When a body undergoes free (undamped) oscillations, it vibrates at what frequency?
It vibrates at its natural frequency.
When does forced oscillations occur?
When a periodic driving force is applied to a system.
What is resonance?
When the driving frequency is equal to the natural frequency of vibration, amplitude of vibration becomes maximum.
Ultrasound may be generated and detected by __________ .
piezo-electric crystals
Explain the principles of the generation of ultrasound waves.
Ultrasonic waves are produced using a piezo-electric crystal such as quartz. A potential difference applied across the crystal causes the centres of the positive and negative charges to move. This causes the crystal to change shape. When an alternating voltage is applied, the crystal vibrates. The frequency of the alternating voltage is the same as the natural frequency of vibration of the crystal, and resonance occurs. This causes the crystal to vibrate with maximum amplitude. Because of the dimensions of the crystal, the oscillations are in the ultrasonic range. Hence, ultrasonic waves are produced in surrounding medium.
Explain the principles of the detection of ultrasound waves.
Ultrasonic transducers also function as ultrasound detectors. When an ultrasonic wave is incident on the unstressed crystal, the pressure variations causes the crystal to vibrate. An alternating potential difference is produced across the crystal. This p.d can then be amplified and processed.
Explain the principles behind the use of ultrasound to obtain diagnostic information about internal body structures.
A pulse of ultrasound is produced by piezo-electric crystal eg. quartz. The pulse is transmitted to the body through a coupling medium. This pulse is reflected at the boundaries between media. The reflected pulse is detected by the ultrasound transmitter. The signal is processed and displayed on a c.r.o. The intensity of the reflected pulse gives information about the boundary. The time delay of the reflected pulse gives information about the depth of the boundary.
Advantage of using shorter-wavelength ultrasound?
Smaller structures inside the body can be detected.
Define specific acoustic impedance.
The product of the density ρ of medium and the speed of sound c in the medium.
Z =ρc
Formula for intensity reflection coefficient
Check notes.
Explain what is meant by intensity reflection coefficient.
The ratio of the reflected intensity to the incident intensity.
Factors affecting intensity of ultrasonic waves passing through medium:
(1) Difference between specific acoustic impedances of media on each side of boundary
(2) Absorption of the ultrasonic wave as it travels through the medium.
Why is a coupling medium used in ultrasound scan?
During the scan, short pulses of ultrasound are transmitted into body. Impedances of
skin and air are very different, so most of ultrasonic waves are reflected at the
air-skin boundary. To reduce the reflection, a coupling medium such as a gel is used.
What is ultrasound A-scan?
A-scan: Transducer is kept in one position. The distance of different boundaries from
the transducer is measured. The reflected pulse of ultrasound is received by transducer and displayed on c.r.o.
What is ultrasound B-scan?
The ultrasound probe for a B-scan consists of many small crystals at different orientations. The signals from all the crystals are combined and processed by a computer, to build up a two-dimensional image. (A series of A-scans are taken from different angles to form a 2-D image).
Advantages of ultrasound
(1) Less health risk to patient compared X-ray
(2) Can examine structures of
transmitted from the transducer into the body (and also return to the transducer after reflection from the soft tissues easily
(3) Equipment is portable.
Disadvantages of ultrasound
(1) Ultrasound therapy, which uses high beam intensities, can be damaging
to bones which have high absorption coefficient.
Formulae to calculate phase difference.
Check notes.
The formula sheet gives an equation for simple harmonic motion.
What does the equation show?
1) The equation shows that a is proportional to x. The constant of proportionality is ω^2.
2) The minus sign shows that acceleration is always in the opposite direction to the displacement.
For s.h.m., sketch a graph of acceleration against time.
Check notes.
Equations for displacement in s.h.m.
Check notes.
Useful applications of resonance.
(1) Microwave cooking: The microwaves have a frequency that matches the natural frequency of vibration of water molecules. The water molecules in the food are forced to vibrate and becomes hotter. The energy spreads through the food and heat it.
(2) Stringed musical instruments, such as guitar, have a hollow wooden box with a hole under the strings. The air resonates and the musical notes are amplified.
(3) Magnetic resonance imaging (MRI): Radio waves with a range of frequencies are used. Atoms in different parts of the body will resonate at particular frequencies. A computer analyse the absorption of radio waves and produces an image.
Situations where resonance should be avoided.
(1) Bridge oscillating during strong winds. If resonance occurs, bridge oscillates with maximum amplitude and bridge collapses.
(2) Buildings may resonate during earthquakes and collapse.
What are the effects of damping on resonance?
Also, sketch a graph to show the effects of damping on resonance.
(i) the amplitude of oscillation at all frequencies is reduced
(ii) the frequency at maximum amplitude decreases slightly
(iii) the peak becomes flatter
Check notes for graph.
Sketch a graph of amplitude against driving frequency, to show resonance.
Check notes.
