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The distance between two successive troughs of a wave is equal to one wavelength (\lambda) One wavelength (\lambda) is defined as the distance between two successive points in the same phase (crest to crest or trough to trough).

f = \(\frac{\text{no of oscillation made}}{t(s)}\) = \(\frac{60}{4}\) = 15 Hz This distance equals 2 wavelengths (because there are 3 troughs, each with 2 intervals between them). 2\(\lambda\) = 15 \(\lambda\) = \(\frac{15}{2}\) = 7.5m V = f\(\lambda\) v = 15 \times 7.5 = 112.5 ms\(^{-1}\)

Polarisation only occurs with a wave whose direction is perpendicular to its vibration (i.e., transverse waves)

T = 0.02 s; \lambda = ?; v = 330 ms⁻¹; f = \(\frac{1}{\text{T}}\) = \(\frac{1}{0.02}\) = 50 Hz But; v = f\lambda \lambda = \(\frac{\text{v}}{\text{f}}\) = \(\frac{330}{50}\) = 6.6 m

The speed of sound in air at a constant temperature is primarily dependent on the temperature of the air rather than the pressure. At a constant temperature, changes in pressure do not significantly affect the speed of sound.

Speed of sound = 60 m/s Time delay = 4 s (light travel time is negligible) Distance = speed \times time = 60 \times 4 = 240 m

Sound waves are mechanical waves, which means they require a medium to travel through. They can travel through all three states of matter: gases (like air), liquids, and solids.

f = 250 Hz; \lambda = 1.3 m; t = 1 s; d = ? v = f\lambda = 250 \times 1.3 = 325 ms\(^{-1}\) v = \(\frac{2d}{\text{t}}\) ∴ d = \(\frac{v \times t}{2}\) = \(\frac{(325 \times 1)}{2}\) = 162.5 m

Quality (overtones) is a characteristic note of a musical instrument that distinguishes it from another note of the same pitch and loudness produced by another instrument.

\lambda = 1 m; v = 200 ms\(^{-1}\); f = ?; f = \(\frac{\text{v}{ \lambda}\) = \(\frac{200}{1}\) = 200 Hz

Short-sightedness (myopia) means distant objects focus in front of the retina, with the far point at 95 cm. A diverging lens (concave) corrects this by creating a virtual image of distant objects (u = \infty) at the far point (v = -95 cm). Using the lens formula: 1/f = 1/v - 1/u = -1/95 - 0, so f = -95 cm (diverging lens with focal length 95 cm).

B. Ciliary muscle. The ciliary muscles control the shape of the lens, allowing the eye to focus on objects at different distances by changing the focal length of the lens.

The tension \( T \) in a string is defined as the force acting along the string. The dimensional formula for force is given by: \([T] = [F] = [M^1 L^1 T^{-2}]\) Thus, the dimensional symbol of tension in a string is: \([T] = [M L T^{-2}]\)

From Faraday's first law, the mass deposited \( m = Z Q \), where \( Z \) is the electrochemical equivalent and \( Q \) is the charge passed. Since the same charge \( Q \) passes through both voltmeters: \(Q = \frac{m_{\mathrm{Cu}}}{Z_{\mathrm{Cu}}} = \frac{m_{\mathrm{Ag}}}{Z_{\mathrm{Ag}}} \) Rearranging for \( Z_{\mathrm{Ag}} \): \(Z_{\mathrm{Ag}} = \frac{m_{\mathrm{Ag}} \cdot Z_{\mathrm{Cu}}}{m_{\mathrm{Cu}}} \) But: \( m_{\mathrm{Cu}} = 0.2 \, \mathrm{g} \), \( m_{\mathrm{Ag}} = 1.2 \, \mathrm{g} \), \( Z_{\mathrm{Cu}} = 0.00028 \, \mathrm{g \, C^{-1}} \) \(Z_{\mathrm{Ag}} = \frac{1.2 \times 0.00028}{0.2} = \frac{0.000336}{0.2} = 0.00168 \, \mathrm{g \, C^{-1}} \)

Magnesium (Mg) belongs to Group 2 (the Alkaline Earth metals) and Period 3 of the periodic table, meaning it has 2 valence electrons and three electron shells, placing it in the s-block.