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AL-LQ-Wave Properties / p.1
1.
(90-IIB-7b)
(b)
Nowadays, worldwide telecommunication is possible using electromagnetic waves of frequencies
(i)
3 – 30 MHz, and
(ii)
3 – 30 GHz.
Describe, with the aid of diagrams, how this is possible for each of the frequency ranges listed.
(5 marks)
AL-LQ-Wave Properties / p.2
2.
(01-IA-3)
Figure 3.1 shows a thin horizontal wire attached to a fixed point A at one end. The wire passes over a
smooth light pulley, and is kept taut by a mass M hanging down at the other end. Movable wooden
wedges B and B’ are placed beneath the wire. A sinusoidal alternating current of variable frequency is
passed into the wire. Strong magnets are placed midway between B and B’ such that the magnetic field
is perpendicular to the wire. As a result the wire is set into vertical vibration.
Figure 3.1
(a) Briefly explain how the vibrations are produced. Name this kind of vibration.
(b) When the frequency of the current is 75Hz and the length of the wire between BB’ is 1.2m, the
appearance of the wire is as shown.
(i)
Find the fundamental frequency and the speed of the waves in the wire.
(ii)
With the length of the wire between BB’ unchanged, the frequency of the current is increased to
a value slightly higher than 75Hz. Explain how to restore the pattern of stationary waves shown.
(c) Would the speed of the waves in the wire increase, decrease or remain unchanged when the
frequency of the current is decreased gradually. Explain Briefly. (No mathematical derivation is
required.)
AL-LQ-Wave Properties / p.3
3.
(01-IB-7)
An earthquake propagates in the form of waves. The quake center produces both longitudinal and transverse
waves, which are known as P waves and S waves respectively. The two types of wave propagate at different
speeds in the earth’s crust. Figure 7.1 shows distance-time graphs for these two waves.
Figure 7.1
(a) With reference to vibrations of particles, state the difference between longitudinal and transverse waves.
(b) (i)
Find the speed of the P waves and of the S waves.
(ii)
The speed of the P waves can be approximated by
E
where E and ρ are respectively the Young

modulus and the average density of the earth’s crust. Estimate E if
  2.5  103 kgm-3.
Three detecting stations A, B and C are located at the vertices of an equilateral triangle as shown in Figure 7.2.
Their mutual separation is 600km. Figure 7.3 shows the records (seismograph traces) of an earthquake recorded by
these stations. Due to the difference in speeds, the P and S waves are detected at different times. Such a time
difference is called the S-P interval. The S-P intervals are respectively 45s, 27s and 18s for stations A, B and C.
Figure 7.2
(c) (i)
(ii)
What evidence in the records shows that station C is closest to the quake center?
Use Figure 7.1 or otherwise to find the distances of stations A and B from the quake center. Which
position in Figure 7.2, X,Y or Z, is the approximate location of the quake center?
(d) The frequency of the quake waves is approximately 5 Hz. It is known that the natural frequencies of bridges F
and G are respectively 6Hz and 12Hz. Explain why bridge F would collapse more easily in an earthquake.
AL-LQ-Wave Properties / p.4
4.
(02-IA-2a)
(a)
A piece of string is fixed at one end to a wall. A wave pulse travels along the string at a speed of
0.5ms-1 towards the fixed end. Its shape at time t = 0 s is shown in Figure 2.1.
(i)
Draw on the above diagram the wave pulse at t = 1 s and t = 2 s.
(ii)
Sketch a graph of the displacement of a point P on the string at a distance of 0.1 m from the
wall during the period of t = 0 s to t = 1 s.
5.
(04-IA-3)
Figure 3.1
Figure 3.1 shows a ship equipped with a sonar to detect objects in the sea. Ultrasonic waves of frequency 25 kHz
are sent towards the seabed. The waves, which propagate at an angle of 50 o to the sea surface, are reflected from a
submarine back to the ship after 0.15s.
Given:
speed of sound in air=340 ms-1
Speed of sound in sea water =1500 ms-1
(a)
Find the wavelength of the ultrasonic waves in sea water. (2 marks)
(b)
Calculate the vertical distance of the submarine beneath the sea surface. (2 marks)
(c)
Some of the ultrasonic waves reflected by the submarine propagate along the dotted line and emerge into air
at X. Calculate the angle of refraction in air. (3 marks)
(d)
Is it possible for ultrasonic waves, at certain angles of incidence, to undergo total internal reflection when
they go from sea water to the air? Explain. (2 marks)
(e)
Explain why microwaves are not suitable for detecting objects in sea water. (1 mark)