Physics Study Guide for the HESI Exam

Waves and Sound

Waves are how energy moves through space or a medium. Sound, light, and water ripples are all types of waves. Some require a medium to travel (such as sound), while others don’t (like light).

Waves

While waves come in many different forms and can even be invisible to the human eye, there are certain terms that are common to all waves:

• crest—the highest point of a wave

• trough—the lowest point of a wave

• amplitude—the maximum height of the wave from its undisturbed position

• wavelength—the distance between a point on one wave and the same point on the next wave (e.g., the distance between two successive peaks or two successive troughs)

• frequency—the number of waves per second, measured in hertz (\(\text{Hz}\)) or \(\text{s}^{–1}\) (referred to as the “inverse second”)

• period—the time it takes for one complete wave cycle to pass a fixed point, measured in seconds (\(\text{s}\))

The following diagram illustrates the main parts of a wave:

Retrieved from: https://commons.wikimedia.org/wiki/File:Water_wave_diagram.jpg

Wave Types

In general, there are two types of waves: mechanical and electromagnetic.

Mechanical Waves

Mechanical waves need a medium (like air, water, or solid material) to travel. They involve the displacement of particles and come in two types:

• transverse waves—In these waves, particles move perpendicular to the wave (e.g., ripples on water).

• longitudinal waves—In these waves, particles move parallel to the wave (e.g., sound waves).

In addition to water and sound waves, other examples of mechanical waves include the movement of a toy spring and seismic waves.

Electromagnetic (EM) Waves

EM waves do not need a medium. They can move through empty space at the speed of light, which is about \(3.0 \times 10^8 \text{ m/s}\) (you should memorize this number).

Some examples of EM waves include light, microwaves, X-rays, and radio waves.

Wave Classification

In waves, energy is transferred by vibrations. Based on their vibrations, we classify waves into two types: longitudinal and transverse.

• longitudinal waves—The vibrations in these waves are in the same direction as the direction of travel. Sound waves and seismic P waves created during earthquakes are examples of longitudinal waves.

• transverse waves—The vibrations in these waves are at \(90\) degrees (right angles) to the direction of travel. Light waves, radio waves, and other electromagnetic waves are examples of transverse waves.

The speed of a wave is measured in meters per second and is given by this equation:

\[v = f \lambda\]

where \(v\) is the wave speed, \(f\) is the frequency, and \(\lambda\) is the wavelength.

When two waves of the same frequency interfere while traveling in opposite directions, they generate a standing wave. These waves contain nodes, which are points with no movement, and antinodes, which are points with maximum movement.

A harmonic is a specific standing wave pattern that fits exactly within a boundary, such as a string fixed at both ends. The \(n\)th harmonic of a standing wave will have a wavelength of:

\[\lambda_n = \frac{2L}{n}\]

where \(n\) is an integer (e.g., \(1,2,3\)) and \(L\) is the length of the vibrating string.

The corresponding frequency is given by:

\[f_n = \frac{nv}{2L}\]

where \(v\) is the speed of the waves on the string.

Let’s try an example problem.

A wave on a string has a frequency of \(10\text{ Hz}\) and a wavelength of \(2\text{ m}\) . What is its speed?

Solution

\[v = f \lambda = 10 \text{ Hz} \times 2 \text{ m} = 20 \text{ m/s}\]

So, the wave travels at \(20\) meters per second.

Light

Light is a form of electromagnetic radiation that travels in waves. It doesn’t need a medium to travel, so it can move through a vacuum, like in space.

The speed of light in a vacuum is \(3 \cdot 10^8\) meters per second, so a light wave with a frequency of \(300\) megahertz (\(\text{ MHz}\)) will have a wavelength of:

\[\frac{3 \cdot 10^8}{300 \cdot 10^6} = 1 \text{ m}\]

Note: A megahertz is equal to 1 million hertz (\(10^6\text{ Hz}\)).

Light behaves as a particle, but it also acts like a wave, meaning it reflects, refracts, and diffracts like waves do.

Light travels much faster than sound. That’s why you see lightning before you hear thunder. When light travels through different materials, its speed slows down, and that’s when bending, or refraction, happens.

Reflection

Reflection is when light bounces off a reflective surface, such as a mirror.

The angle of incidence (where light hits a surface) is equal to the angle of reflection (the angle it bounces off). This is known as the law of reflection and is shown in the diagram below:

Retrieved from: https://openstax.org/books/college-physics-2e/pages/25-2-the-law-of-reflection

Refraction

Refraction is the bending of light as it passes from one medium into another, such as from air to water.

The normal is a line perpendicular (at 90 degrees) to the boundary between the media. This is shown below, the diagram labeled (a) represents light bending toward the normal, and the diagram labeled (b) represents light bending away from the normal:

Retrieved from: https://openstax.org/books/university-physics-volume-3/pages/1-3-refraction

Snell’s Law

Refraction can be calculated using Snell’s law. This law describes how much light will bend when it enters a different medium and is expressed mathematically as follows:

\[n_1 \cdot \sin (\theta_1) = n_2 \sin (\theta_2)\]

where \(n_1\) and \(n_2\) are the indices of refraction for each medium, \(\theta_1\) is the angle of incidence, and \(\theta_2\) is the angle of refraction.

Index of Refraction

The index of refraction (\(n\)) tells you how much a material slows down light. When optometrists are determining the correct lenses for a patient, they must be able to calculate the index of refraction. It is found by dividing the speed of light in a vacuum (\(c\)) by the speed of light in the material (\(v\)):

\[n = \frac{c}{v}\]

Note: You should remember that the speed of light in a vacuum is \(3 \times 10^8\) meters per second.

We’ll try an example problem with this formula.

An optometrist is testing a new type of lens materials for eyeglasses. She measured the speed of light of the material and finds it to be \(2.0 \times 10^8 \text{ m/s}\). What is the index of refraction of this lens material?

Solution

\[n = \frac{c}{v} = \frac{3.0 \times 10^8 \text{ m/s}}{2.0 \times 10^8 \text{ m/s}} = 1.5\]