Physics 2013 Jamb Examination

Waves are categorised based on the relationship between the direction of propagation and the direction of particle displacement. In a transverse wave, the particles of the medium vibrate perpendicularly (at right angles) to the direction of the wave's travel. In a longitudinal wave, the particles vibrate parallel to the direction of the wave's travel, creating compressions and rarefactions. While both types can share the same frequency, amplitude, or period, the fundamental mechanical difference lies in how the medium's particles move relative to the wave's path.

The velocity of sound in a gas is directly proportional to the square root of its absolute temperature (measured in Kelvins). The relationship is given by: \[ \frac{v_1}{\sqrt{T_1}} = \frac{v_2}{\sqrt{T_2}} \]Given:
\(v_1 = 340 \text{ ms}^{-1}\)
\(T_1 = 0 + 273 = 273 \text{ K}\)
\(T_2 = 100 + 273 = 373 \text{ K}\)
Substituting the values:\[ v_2 = v_1 \times \sqrt{\frac{T_2}{T_1}} \]\[ v_2 = 340 \times \sqrt{\frac{373}{273}} \]\[ v_2 = 340 \times \sqrt{1.366} \]\[ v_2 = 340 \times 1.1688 \]\[ v_2 \approx 397.4 \text{ ms}^{-1} \]Therefore, the velocity at 100°C is approximately 397ms\(^{-1}\).

For a stretched string (like in a sonometer), the harmonics are integral multiples of the fundamental frequency \(f_0\). The harmonics are numbered \(f_1, f_2, f_3...\), where \(f_1\) is the fundamental frequency. Overtones start after the fundamental: the 1st overtone is the 2nd harmonic (\(2f_0\)), the 2nd overtone is the 3rd harmonic (\(3f_0\)), and so on.
The formula for the frequency of the \(n\)-th overtone is:\[ f_n = (n + 1)f_0 \]For the 5th overtone (\(n = 5\)):\[ f_5 = (5 + 1) \times 450 \]\[ f_5 = 6 \times 450 \]\[ f_5 = 2700 \text{ Hz} \]

The pinhole camera works on the principle of similar triangles, where the magnification \(M\) is the ratio of image height \(h_i\) to object height \(h_o\), which is also equal to the ratio of image distance \(v\) to object distance \(u\).\[ M = \frac{h_i}{h_o} = \frac{v}{u} \]Given:
\(h_o = 1.5 \text{ m}\)
\(u = 3 \text{ m}\)
\(v = 0.1 \text{ m}\)
Solving for \(h_i\):\[ h_i = \frac{h_o \times v}{u} \]\[ h_i = \frac{1.5 \times 0.1}{3} \]\[ h_i = \frac{0.15}{3} \]\[ h_i = 0.05 \text{ m} \]

The centre of curvature (C) is the centre of the sphere from which the mirror was cut. Any line passing through C to the surface of the mirror is a radius, and therefore is normal (perpendicular) to the mirror's surface at that point. Since the ray strikes the mirror normally, the angle of incidence is 0°. According to the law of reflection, the angle of reflection must also be 0°, meaning the ray reflects back along its original path. Note: While the ray turns 180° in direction, the physical 'angle of reflection' (measured relative to the normal) is 0°.

Total Internal Reflection (TIR) can only occur when two conditions are met:
1. Light must be travelling from a more optically dense medium (higher refractive index) to a less optically dense medium (lower refractive index).
2. The angle of incidence must exceed the critical angle.
Comparing the refractive indices:
\(n_{\text{glass}} \approx 1.5\), \(n_{\text{water}} \approx 1.33\), \(n_{\text{air}} \approx 1.0\).
In option B, light travels from water (1.33) to glass (1.5). Since it is moving from a less dense to a more dense medium, the light ray will bend towards the normal and TIR is physically impossible regardless of the angle.

The total magnification of a compound microscope is the product of the magnification of the objective lens (\(M_o\)) and the magnification of the eyepiece (\(M_e\)).\[ M_{\text{total}} = M_o \times M_e \]Given:
\(M_o = 4\)
\(M_e = 7\)\[ M_{\text{total}} = 4 \times 7 = 28 \]The microscope magnifies the object 28 times.

In a prism, shorter wavelengths of light slow down more and are refracted (bent) more than longer wavelengths. Red light has the longest wavelength in the visible spectrum and is deviated the least, while violet/blue light has shorter wavelengths and is deviated the most. The standard order of increasing deviation follows the ROYGBIV spectrum (Red, Orange, Yellow, Green, Blue, Indigo, Violet). Therefore, the correct sequence showing increasing deviation is red → green → blue.

The force \(F\) exerted on a charge \(q\) in an electric field of intensity \(E\) is given by the formula:\[ F = qE \]Given:
\(q = 1.5 \times 10^{-19} \text{ C}\)
\(E = 10^{5} \text{ Vm}^{-1}\)
Calculating the force:\[ F = (1.5 \times 10^{-19}) \times 10^{5} \]\[ F = 1.5 \times 10^{(-19 + 5)} \]\[ F = 1.5 \times 10^{-14} \text{ N} \]

An induction coil contains a 'breaker' or interrupter that rapidly opens and closes the circuit. When the circuit is broken, the collapsing magnetic field in the primary coil induces a high voltage, which can cause a spark to jump across the contact points, damaging them over time. A capacitor is connected across the contact breaker to absorb this energy and suppress the sparking. It also helps the magnetic field to collapse more rapidly, which increases the secondary voltage induced.