Oscillations

Question 1

Period of an oscillation

Answer 1

The time taken to complete one oscillation.

Question 2

Frequency

Answer 2

The number of oscillations per unit time.

Question 3

f =

Answer 3

f = 1 / T

Question 4

Displacement

Answer 4

Distance from the equilibrium position.

Question 5

Amplitude

Answer 5

Maximum displacement.

Question 6

Simple harmonic motion

Answer 6

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.

Question 7

In s.h.m., the acceleration is always directed towards _____________.

Answer 7

the equilibrium position.

Question 8

Angular frequency

Answer 8

ω = 2πf

ω = 2π / T

Question 9

Where does maximum speed occur?

Answer 9

At the equilibrium position,

at x = 0

Question 10

How do you get the equation for kinetic energy in s.h.m.?

Answer 10

Check notes.

Use KE = 1/2mv^2 and velocity in s.h.m. from formulae sheet.

Question 11

Potential energy in s.h.m.?

Answer 11

Check notes.

Question 12

Total energy in s.h.m.?

Answer 12

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

Question 13

Sketch, on the same axis, the graph of KE, PE and total energy against displacement.

Answer 13

Check notes.

Question 14

What are free oscillations?

Answer 14

Oscillations where there are no resistive forces acting on the oscillating system.

Question 15

What is damping?

Answer 15

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.

Question 16

What is the effect of light damping?

Answer 16

It causes the amplitude of vibration to decrease gradually.

Check graph in notes.

Question 17

What is the effect of critical damping?

Answer 17

It causes the displacement to be reduced to zero in the shortest time possible, without any oscillation of the object.
Check graph in notes.

Question 18

What is the effect of overdamping?

Answer 18

It also causes an exponential reduction in displacement, but over a greater time (compared to critical damping).
Check graph in notes.

Question 19

When a body undergoes free (undamped) oscillations, it vibrates at what frequency?

Answer 19

It vibrates at its natural frequency.

Question 20

When does forced oscillations occur?

Answer 20

When a periodic driving force is applied to a system.

Question 21

What is resonance?

Answer 21

When the driving frequency is equal to the natural frequency of vibration, amplitude of vibration becomes maximum.

Question 22

Ultrasound may be generated and detected by __________ .

Answer 22

piezo-electric crystals

Question 23

Explain the principles of the generation of ultrasound waves.

Answer 23

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.

Question 24

Explain the principles of the detection of ultrasound waves.

Answer 24

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.

Question 25

Explain the principles behind the use of ultrasound to obtain diagnostic information about internal body structures.

Answer 25

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.

Question 26

Advantage of using shorter-wavelength ultrasound?

Answer 26

Smaller structures inside the body can be detected.

Question 27

Define specific acoustic impedance.

Answer 27

The product of the density ρ of medium and the speed of sound c in the medium.
Z =ρc

Question 28

Formula for intensity reflection coefficient

Answer 28

Check notes.

Question 29

Explain what is meant by intensity reflection coefficient.

Answer 29

The ratio of the reflected intensity to the incident intensity.

Question 30

Factors affecting intensity of ultrasonic waves passing through medium:

Answer 30

(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.

Question 31

Why is a coupling medium used in ultrasound scan?

Answer 31

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.

Question 32

What is ultrasound A-scan?

Answer 32

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.

Question 33

What is ultrasound B-scan?

Answer 33

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).

Question 34

Advantages of ultrasound

Answer 34

(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.

Question 35

Disadvantages of ultrasound

Answer 35

(1) Ultrasound therapy, which uses high beam intensities, can be damaging
to bones which have high absorption coefficient.

Question 36

Formulae to calculate phase difference.

Answer 36

Check notes.

Question 37

The formula sheet gives an equation for simple harmonic motion.
What does the equation show?

Answer 37

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.

Question 38

For s.h.m., sketch a graph of acceleration against time.

Answer 38

Check notes.

Question 39

Equations for displacement in s.h.m.

Answer 39

Check notes.

Question 40

Useful applications of resonance.

Answer 40

(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.

Question 41

Situations where resonance should be avoided.

Answer 41

(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.

Question 42

What are the effects of damping on resonance?

Also, sketch a graph to show the effects of damping on resonance.

Answer 42

(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.

Question 43

Sketch a graph of amplitude against driving frequency, to show resonance.

Answer 43

Check notes.