# Chapter 20 ```Cambridge International AS and A level Physics
d
3
T will increase as the mass increases. When the mass is
displaced to the side and released, a greater mass will
accelerate less (F = ma) and so it will take longer to complete
an oscillation. (The factor m in the equation in part c will not
cancel out.)
Exam-style questions
1
a–c
2
a
period = 100 ms; frequency = 10 Hz
b
x = 15 sin 20πt or x = 15 sin 63t
c
maximum velocity = ω x0 = 20π &times; 15 = 942 mm s −1 = 0.94 m s −1
d
F0 = mω 2 x0 = 17 &times; (20π)2 &times; 15 &times; 10 −3 = 1.01 &times; 103 N
a
Simple harmonic motion: motion of an oscillator in which its
acceleration is directly proportional to its displacement from
its equilibrium position and is directed towards that position.
b
Equilibrium position is when the mass is stationary.
c
v
F
x
0
Acceleration
d
X
0
0
t
0
Time
32
e
x0
0
0
t
Acceleration is always in the opposite direction to the
displacement because the restoring force is always opposite
to the displacement.
e
3.0 cm
f
ω2 =
g
T=
4
so ω = 11.5 rad s −1
0.03
2π
ω
= 0.54 s
Chapter 20:
f
The amplitude of the oscillations reduces to zero more quickly
as the density of the air increases.
Communication systems
g
Critical damping is observed when the damped system
returns to equilibrium without oscillating.
Exercise 20.1 Modulation
a
The natural frequencies are equal.
b
resonance
c
Yes, energy is conserved. The energy of the first pendulum
is transferred entirely to the second one (via the strings),
and then back again to the first. (Of course, energy is always
conserved!)
d
The natural frequencies of the two pendulums would be
different so the second pendulum would not be driven at its
natural frequency.
1
4
d
a
b
The carrier wave is a high frequency signal. The amplitude
is made to increase and decrease in synchrony with the
input signal.
c
frequency
2
a
3
a
Record a value (usually of voltage) of the signal at one instant.
b
2.07 &times; 109
c
To recover the analogue signal in its original form from the
digital signal.
a
a signal that is continuously variable within limits
b, c
3
4
b
The carrier wave is a high frequency signal. The frequency is
made to increase and decrease in synchrony with the input
signal.
c
amplitude
a
less interference or less noise; larger bandwidth or better quality
b
smaller bandwidth means more stations in a given frequency
range; cheaper radio sets as electronics less complex; covers
a greater area as wavelengths used are longer
a
2.0 &times; 10 s
b
2.0 &times; 10 −4 s
c
Power
−5
4
0
5
6
7
b
3
0
c
Time 0 1 0 1 0 0 1 1 0 1
d
digital-to-analogue converter
e
The largest 4-bit number is 1111 = 15 and so, including 0, there
are 16 possible values.
f
If S changes V1 in between the samples it has no effect on the
g
have more bits and sample more frequently
h
The parallel-to-serial converter takes the 4 bits of each digital
sample and then emits it as a series of bits, one after the
other. The serial-to-parallel converter takes the series of bits
and converts them into the 4 separate bits.
a
random and unwelcome power that distorts the
transmitted signal
b
as long as the noise does not make a 0 too close to a 1 or a 1
too close to a 0 then 0 and 1 can be recognised
c
needs fewer amplifiers or they can be further apart
Exercise 20.3 Channels of communication
45
50
55
Frequency / kHz
1
a
polar orbit
geostationary
orbit
d
a band of frequencies higher than or lower than the carrier
frequency, produced as a result of the modulation process
e
45 and 55 kHz
f
10 kHz
a
8600 Hz
b
weather forecasting; spying; monitoring the surface
b
31
c
one day or 24 hours
a
6.0 V
d
b
860 kHz
The satellite orbits in the same time as the Earth rotates and
is fixed over a point on the equator.
c
740 kHz
e
Polar regions
d
20 Hz
a
a
6.5 V
linking a ground station to a satellite; t.v. from a satellite;
mobile phones
b
5.5 V
b
connecting an aerial to a television; computer network
connections; audio and video connections
c
800 kHz
c
d
5000
older telephone and computer connections; linking hi-fi to
a loudspeaker
a
wire pair: two wires twisted together
coaxial cable: copper braid on outside, core is a copper wire
separated from the core by an insulator
b
Signal in one wire pair is picked up by a neighbouring
wire pair.
c
Outer of coaxial cable is earthed and shields the core from
noise or external signals.
Exercise 20.2 Analogue and digital signals
1
Voltage / V
2
a
a basic unit of information storage stored as a binary digit 0 or 1
b
1011
c
three
d
the first one
e
five
2
3
33
Cambridge International AS and A level Physics
4
5
a
They pass through the ionosphere with little reflection and
can carry large amounts of information.
b
To prevent the satellite’s high power transmitted signal
swamping reception of the very low power signal received
from Earth.
c
Space wave to satellite, sky wave reflected from ionosphere,
surface wave travels direct.
d
Ionospheric reflection varies as layers of ions vary in height
and density according to the time of day.
iii
iv
b
Optic fibres have a wide bandwidth and large transmission
capacity. Signal power losses are relatively small and allow longer
distances between regenerator amplifiers. The diameter, weight
and cost of fibre optic cables are much less than those of metal
cables. Optic fibres have negligible ‘cross-talk’ and do not pick
up electromagnetic interference.
c
2
34
a
2.0
b
15.8
a
190 or −190 dB
b
Logarithm provides a smaller number or attenuation in series
increases as the signal reduces and the noise remains,
approximately, constant
i
1.52 mW
ii
27 dB
iii
4.5 km
i
less attenuation with fibre optic cable; longer distance
before signal attenuated to minimum acceptable signal;
also, noise may be lower on an optic fibre
ii
larger bandwidth; larger transmission capacity; smaller
diameter, weight and cost; negligible ‘cross-talk’; less
electromagnetic interference/noise
Chapter 21:
20 dB
4
3.0 &times; 10 −14 W
5
a
6.0 &times; 10 −2 mW or 6.0 &times; 10 −5 W
b
49.6 km
7
Thermal physics
Exercise 21.1 Kinetic model and internal energy
1
3
6
a
4.6 &times; 10 −4 W
b
7.3 &times; 10 −3 W
a
240 dB
b
six
2
Exam-style questions
1
a
most closely together: solid
farthest apart: gas
b
They vibrate with greater amplitude; their velocity is greater
as they oscillate through the midpoint of their oscillation.
c
attractive
d
Potential energy increases as particles are pulled apart;
energy is being added to the material.
e
greater separation: greater potential energy
greater speed: greater kinetic energy
a
greater amplitude of oscillation
b
greater separation
c
The potential and kinetic energies of the atoms have
increased.
a
Amplitude of carrier wave varies in synchrony with the
displacement of the information signal.
a
B
b
i
spectrum A as only the carrier wave is present
b
ii
spectrum C as the carrier and one signal in the two
sidebands is present
More molecules in B have sufficient kinetic energy to escape
from the surface of the water.
c
iii
spectrum B as the carrier and two sidebands are present;
music has a number of different frequencies and thus
different lines in the sidebands
Evaporation means that the molecules with the highest
kinetic energies escape, so the average kinetic energy of the
molecules remaining in the liquid decreases.
d
More molecules escape initially from B (see answer to b), so
the average kinetic energy of the molecules remaining in the
liquid decreases more quickly.
c
d
2
⎛ signal power ⎞
10 lg ⎜
⎝ noise power ⎟⎠
v
Exercise 20.4 Attenuation
1
thermal vibrations of the atoms of the material; electrical
interference (for example, wire acts as aerial); induced
emf caused by change in magnetic field
a
i
200 kHz
ii
3.0 kHz
iii
12 kHz
3
a
average speed of the particles increases
disadvantages: more noise; more interference; less
bandwidth; lower quality
b
total kinetic energy increases
c
temperature of the gas increases
advantages: longer range; fewer repeaters or transmitters
needed; less complex electronics; cheaper
d
a force is doing work
e
2.4 J
i
the gradual loss of power along a wire
ii
thermal energy lost in the wire
4
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