Explain the construction of a spherical wavefront by using Huygens' principle.
Huygens' principle states that every point on a wavefront acts as a source of secondary spherical wavelets. As these wavelets spread outward, they form a new wavefront. For a spherical wavefront, the wavelets originate from a point source, and as they travel, they create spherical surfaces around the source. The radius of each spherical wavefront expands over time, and the new wavefront is tangent to the wavelets.
Derive an expression for the equation of stationary wave on a stretched string. Show that the distance between two successive nodes or antinodes is \( \frac{\lambda}{2} \).
Two tuning forks having frequencies 320 Hz and 340 Hz are sounded together to produce sound waves. The velocity of sound in air is 340 m/s. Find the difference in wavelength of these waves.
Derive an expression for energy stored in a charged capacitor. A spherical metal ball of radius 15 cm carries a charge of 2μC. Calculate the electric field at a distance of 20 cm from the center of the sphere.
Draw a neat labelled diagram of Ferry's perfectly black body. Compare the rms speed of hydrogen molecules at 227°C with rms speed of oxygen molecules at 127°C. Given that molecular masses of hydrogen and oxygen are 2 and 32, respectively.
Distinguish between an ammeter and a voltmeter. (Two points each).
The displacement of a particle performing simple harmonic motion is \( \frac{1}{3} \) of its amplitude. What fraction of total energy is its kinetic energy?
Using the geometry of the double slit experiment, derive the expression for the fringe width of interference bands.
An alternating voltage is given by \( e = 8 \sin(628.4 t) \).
Find:
(i) Peak value of e.m.f.
(ii) Frequency of e.m.f.
(iii) Instantaneous value of e.m.f. at time \( t = 10 \, {ms} \)