波的性質、疊加與駐波：練習題

In wave physics, a line or surface that connects points that are all in phase is known as a:

A ray of monochromatic light travels from a transparent liquid into air. The speed of light in the liquid is \( 2.25 \times 10^8 \text{ m s}^{-1} \) and the speed of light in air is \( 3.00 \times 10^8 \text{ m s}^{-1} \). What is the critical angle for the liquid-air interface?

In a photoelectric effect experiment, monochromatic light is incident on a metal surface. If the intensity of the incident light is doubled while its frequency is kept constant and above the threshold frequency, which of the following happens?

Two points on a progressive wave are separated by a distance equal to half a wavelength. What is the phase difference between these two points?

A ray of light travels through a dense liquid with a refractive index of \( 1.62 \) towards a boundary with air (refractive index \( \approx 1.00 \)). Calculate the critical angle for total internal reflection at this boundary.

A stationary wave is formed on a string fixed at both ends and is vibrating in its fourth harmonic. Determine the number of nodes and antinodes present along the length of the string.

A string of length \( 1.5 \text{ m} \) is fixed at both ends and vibrates in its third harmonic. If the speed of transverse waves on the string is \( 120 \text{ m s}^{-1} \), calculate the frequency of the vibration.

A diffraction grating has \( 800 \text{ lines per mm} \). Light is incident normally and the third-order maximum is at \( 70^{\circ} \). Show by calculation whether a fourth-order maximum can be observed.

Explain the difference between longitudinal and transverse waves in terms of particle displacement and pressure variation. Provide one example for each type of wave.

A ray of monochromatic light is incident on the face of a right-angled glass prism at an angle of \( 42.0^{\circ} \) to the normal. The refractive index of the glass is \( 1.62 \).
(a) Calculate the angle of refraction as the light enters the prism.
(b) After entering, the ray travels through the glass and meets the second face of the prism. Calculate the critical angle for the glass-air interface.
(c) Determine whether the light will undergo total internal reflection at the second face if it is incident on that face at an angle of \( 45.0^{\circ} \) to the normal.