Saturday, June 24, 2017

What, to two significant figures, are the period, the frequency and the amplitude of the wave represented by the graph?






Question 1
What, to two significant figures, are the period, the frequency and the amplitude of the wave represented by the graph?


period / s        frequency / Hz           amplitude / m
A          0.0027             370                              0.0067
B          0.0031             320                              0.013
C         0.0035             290                              0.0067
D         0.0042             240                              0.013





Reference: Past Exam Paper – June 2014 Paper 12 Q22





Solution:
Answer: C.
A graph of displacement against time is given. The y-axis gives displacement in ‘m’ and the x-axis gives time in ‘ms’.

Period can be directly obtained from the time axis.
3.5 waves correspond to 12.1 ms.
3.5 T = 12.1×10-3 s
Period T = 12.1×10-3 / 3.5 = 0.0035 s

Frequency = 1 / T = 1 / 0.0035 = 290 Hz

Amplitude is the maximum displacement. This can be obtained from the y-axis.
Amplitude = 6.7 mm = 0.0067 m

Saturday, May 13, 2017

The diagram shows a circuit containing three resistors in parallel. The battery has e.m.f. 12 V and negligible internal resistance.




Question 2
The diagram shows a circuit containing three resistors in parallel.

The battery has e.m.f. 12 V and negligible internal resistance. The ammeter reading is 3.2 A.
What is the resistance of X?

A 2.1 Ω           B 4.6 Ω           C 6.0 Ω           D 15 Ω





Reference: Past Exam Paper – November 2008 Paper 1 Q35





Solution:
Answer: D.
For a parallel combination, the p.d. across each branch is equal and in this case, the p.d. across each branch is equal to the e.m.f. of 12 V.

To know the resistance of X, we need to know the p.d. across it (= 12V) and the current flowing through it (unknown).
The current of 3.2A coming from the terminal of the battery splits at the junction.
Current across the 10Ω resistor = V/R = 12/10 = 1.2 A
Current through X = 3.2 – 1.2 – 1.2 = 0.8 A

From Ohm’s law, Resistance of X = V/I = 12 / 0.8 = 15 Ω

Monday, May 1, 2017

A uniform string is held between a fixed point P and a variable-frequency oscillator, as shown in Fig. 5.1.




Question 1
A uniform string is held between a fixed point P and a variable-frequency oscillator, as shown in Fig. 5.1.

Fig. 5.1
The distance between point P and the oscillator is L.
The frequency of the oscillator is adjusted so that the stationary wave shown in Fig. 5.1 is formed.
Points X and Y are two points on the string.
Point X is a distance 1/8 L from the end of the string attached to the oscillator. It vibrates with frequency f and amplitude A.
Point Y is a distance 1/8 L from the end P of the string.

(a) For the vibrations of point Y, state
(i) the frequency (in terms of f ), [1]
(ii) the amplitude (in terms of A). [1]

(b) State the phase difference between the vibrations of point X and point Y. [1]

(c) (i) State, in terms of f and L, the speed of the wave on the string. [1]

(ii) The wave on the string is a stationary wave.
Explain, by reference to the formation of a stationary wave, what is meant by the
speed stated in (i). [3]





Reference: Past Exam Paper – November 2009 Paper 22 Q5





Solution 1:
(a)
(i) f                                          [B1]

(ii) A                                        [B1]
{Amplitude means maximum displacement.}


(b) 180o           or π rad            (unit necessary)                       [B1]
{When talking about the phase of a point, we need to consider its displacement and the direction of motion/vibration.
Phase difference between 2 points means the difference in phase about the 2 points.
Point X and Y are at the same displacement (one is +ve and the other -ve). However, they moving in opposite direction. So, they are out of phase (phase difference = 180°).}

[For more explanation on Phase difference, see solution 318 at http://physics-ref.blogspot.com/2015/01/physics-9702-doubts-help-page-55.html]


(c) (i) Speed of wave = f x L                                                  [B1]

(ii)
The wave is reflected at the end / at P.                       [B1]
EITHER The incident and reflected waves interfere OR the two waves travelling in opposite directions interfere.                                              [M1]
The speed is the speed of incident or reflected wave / one of these waves.  [A1]

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