Physics: Waves, Sound, and Light - Reflection, Refraction, and Diffraction

A sound wave has a frequency of $500 \text{ Hz}$ and travels at a speed of $340 \text{ m/s}$. Calculate the wavelength $\lambda$ of the sound wave.

Using the wave equation $v = f \lambda$, we rearrange to find $\lambda$: $\lambda = \frac{v}{f}$ $\lambda = \frac{340}{500}$ $\lambda = 0.68 \text{ m}$

The wavelength is the distance between two consecutive compressions in a sound wave. By dividing the velocity by the frequency, we determine this distance is $0.68$ meters.

A ray of light strikes a plane mirror at an angle of $35^\circ$ to the surface of the mirror. What is the angle of reflection?

First, find the angle of incidence $\theta_i$ relative to the normal: $\theta_i = 90^\circ - 35^\circ = 55^\circ$ According to the Law of Reflection: $\theta_r = \theta_i = 55^\circ$

Angles in reflection are always measured from the normal. Since the ray is $35^\circ$ from the surface, it is $55^\circ$ from the normal. Thus, the reflected ray is also $55^\circ$ from the normal.

If the speed of light in a vacuum is $3 \times 10^8 \text{ m/s}$ and the refractive index of a glass block is $1.5$, calculate the speed of light $v$ inside the glass.

Using the formula for refractive index $n = \frac{c}{v}$, we rearrange to solve for $v$: $v = \frac{c}{n}$ $v = \frac{3 \times 10^8}{1.5}$ $v = 2 \times 10^8 \text{ m/s}$

The refractive index tells us how much the medium slows down light. A higher index means light travels slower. In this case, light slows down from $3 \times 10^8 \text{ m/s}$ to $2 \times 10^8 \text{ m/s}$.