Waves & Sound — Part 2: 16 MCQs with Explanations

For a string fixed at both ends, frequency f ∝ 1/L. If length L is doubled, the frequency becomes half. Therefore, new frequency = 256 Hz / 2 = 128 Hz.

When a source of sound and an observer move towards each other, the number of wavefronts received per second increases. This results in an increase in the observed frequency.

The energy (E) of a photon is directly proportional to its frequency (f): E = hf. Since frequency f = c/λ, where c is the speed of light and λ is the wavelength, we get E = hc/λ.

In a half-wave rectifier, only one half of the input AC cycle is allowed to pass. The output waveform consists of pulses for each positive half-cycle. Therefore, the frequency of the output ripple is the same as the input AC frequency (e.g., 50 Hz).

Heat is transferred via three main modes: conduction (through solids), convection (through fluids), and radiation (via electromagnetic waves). Absorption is a process by which a material takes in energy, not a mode of transfer.

Sound travels fastest in solids because the particles are more tightly bound, allowing vibrations to transfer more quickly. It is slowest in gases. Speed in steel >> speed in water >> speed in air.

A stationary wave (standing wave) is characterized by points of zero displacement called nodes and points of maximum displacement called antinodes, formed by the superposition of two identical waves traveling in opposite directions.

The photoelectric effect could not be explained by the wave theory of light. Einstein explained it using the quantum theory, proposing that light consists of discrete packets of energy called photons.

At resonance, the inductive reactance (XL) equals the capacitive reactance (XC). They cancel each other out, so the impedance Z = √(R² + (XL - XC)²) becomes purely resistive and equal to R, which is the minimum possible impedance.

The electromagnetic spectrum is arranged by frequency and wavelength. Gamma rays have the highest frequency and shortest wavelength, followed by X-rays and then ultraviolet rays.

When light enters a denser medium (glass) from a rarer medium (air), its speed (v) and wavelength (λ) decrease. However, its frequency (f) remains constant because it depends on the source. v = fλ, so if v decreases, λ must also decrease.

At resonance, the circuit is purely resistive because the inductive and capacitive reactances cancel out. For a purely resistive circuit, the phase angle φ = 0°, so the power factor cos φ = 1.

Polarization is a property of transverse waves. Longitudinal waves (like sound) cannot be polarized because their vibration is parallel to the direction of propagation. Polarization confirms that light waves are transverse in nature.

The stopping potential (V₀) is given by eV₀ = hf - φ, where f is the frequency and φ is the work function. While it depends on the work function, for a given metal, it varies linearly with the frequency of the incident light. It is independent of intensity.

When two identical waves traveling in opposite directions superimpose, they produce a stationary wave (standing wave). The wave appears to be standing still with nodes and antinodes.

In Pakistan, as in many parts of the world (Europe, Asia), the standard frequency for alternating current (AC) mains electricity is 50 Hz.