14.1 Properties of Wave Pulses and Waves

TLDR

A wave moves energy from one place to another without carrying matter along with it. In AP Physics 2, you need to describe wave properties like amplitude, speed, and direction of disturbance, tell mechanical and electromagnetic waves apart, and separate transverse waves from longitudinal waves.

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Why This Matters for the AP Physics 2 Exam

This topic builds the vocabulary and core models you use for the rest of Unit 14, which counts for about 12 to 15 percent of the exam. The wave properties here show up when you describe diagrams, compare two scenarios, and explain how a change in one quantity affects another. Multiple-choice questions often ask you to analyze wave representations, and the free-response section includes a Translation Between Representations question where you connect sketches, graphs, equations, and verbal descriptions. Getting comfortable with amplitude, wave speed, and wave type now makes periodic waves, sound, and interference much easier later.

Key Takeaways

• A wave transfers energy without transferring matter; a wave pulse is a single disturbance, while a wave is a continuous, periodic disturbance with a defined wavelength and frequency.
• Mechanical waves need a medium to travel through; electromagnetic waves do not, so they can move through a vacuum at $c = 3.00 \times 10^{8} \text{ m/s}$.
• Wave speed depends on the wave type and the medium. On a string, $v_{\text{string}} = \sqrt{\frac{F_{T}}{m/\ell}}$, and the speed of sound increases as a medium's temperature rises.
• In a transverse wave, the disturbance is perpendicular to the direction the wave travels; in a longitudinal wave, the disturbance is parallel to it.
• Sound is a mechanical longitudinal wave with compressions (high pressure) and rarefactions (low pressure).
• Amplitude is the maximum displacement from equilibrium. Greater amplitude means more energy carried and, for sound, greater loudness.

Physical Properties of Waves

Energy Transfer Without Matter

Waves move energy between two locations without moving matter from one place to another. Picture ocean waves: the wave travels a long distance, but the water mostly moves up and down instead of traveling with the wave.

• A wave pulse is a single disturbance that transfers energy from one point to another without transferring matter.
• A wave is modeled as a continuous, periodic disturbance with a well-defined wavelength and frequency.
• The energy carried can take different forms depending on the wave type, such as mechanical energy in water waves or electromagnetic energy in light.

Mechanical vs Electromagnetic Waves

Mechanical waves need a physical medium to travel through. Electromagnetic waves do not.

• Mechanical waves, like sound or water waves, need particles of matter to pass energy along.
• These particles oscillate and hand the disturbance off to neighboring particles.
• Electromagnetic waves, like light, radio waves, and X-rays, are made of oscillating electric and magnetic fields.
• They can travel through a vacuum, which is why sunlight reaches Earth across empty space.

Wave Speed in Media

How fast a wave travels depends on both the type of wave and the properties of the medium it moves through.

• All electromagnetic waves travel through a vacuum at the same speed: $c = 3.00 \times 10^{8} \text{ m/s}$, the speed of light.
• For a wave pulse or wave moving along a string, the speed depends on:
  • The tension in the string, $F_{T}$
  • The mass per unit length of the string, $m/\ell$
  • Together these give $v_{\text{string}} = \sqrt{\frac{F_{T}}{m/\ell}}$
• In a given medium, sound waves travel faster as the temperature of the medium increases.

Transverse Waves

In a transverse wave, the disturbance is perpendicular to the direction the wave travels.

• A wave on a string is the classic example: the string moves up and down while the wave travels horizontally.
• Light and other electromagnetic waves are transverse, with electric and magnetic fields oscillating perpendicular to the direction of travel.
• Because the disturbance is perpendicular to propagation, transverse waves can be polarized (covered more in a later topic).

Longitudinal Waves

In a longitudinal wave, the disturbance is parallel to the direction the wave travels.

• Sound waves are modeled as mechanical longitudinal waves. 🔊
• As sound moves through air, it creates regions of compression (high pressure) and rarefaction (low pressure).
• These pressure changes make air molecules oscillate back and forth along the same direction the wave travels.

Wave Amplitude

Amplitude is the maximum displacement of a wave from its equilibrium position, and it connects directly to the energy the wave carries.

• For a transverse wave on a string, amplitude is the maximum distance the string moves above or below equilibrium.
• For a longitudinal pressure wave like sound, amplitude can be measured by the maximum increase or decrease in pressure from equilibrium pressure.
• The loudness of a sound increases with increasing amplitude.
• The energy carried by a wave increases with increasing amplitude. 📈

How to Use This on the AP Physics 2 Exam

Problem Solving

When you calculate wave speed on a string, start by finding the linear mass density $m/\ell$ before plugging into the formula. Keep units consistent so your answer comes out in m/s.

• Identify what the medium tells you. For a string, you need tension and mass per length. For electromagnetic waves in a vacuum, the speed is always $c$.
• Watch functional dependence. If a question doubles the tension, the speed changes by a factor of $\sqrt{2}$, not 2, because $F_T$ is under the square root.

Free Response

The Translation Between Representations question asks you to move between sketches, graphs, equations, and words. For this topic, that often means reading amplitude or wavelength off a graph, or describing a wave in words and matching it to the right equation or diagram.

• Label transverse vs longitudinal correctly by checking the direction of the disturbance against the direction of propagation.
• When you justify a claim about energy, tie it back to amplitude. More amplitude means more energy carried.

Common Trap

Questions often try to get you to say matter travels with the wave. Be precise: energy moves, matter oscillates in place.

Common Misconceptions

• Waves carry matter from place to place. They do not. A wave transfers energy while the particles of the medium oscillate around their equilibrium positions and stay roughly in place.
• All waves need a medium. Mechanical waves do, but electromagnetic waves can travel through a vacuum.
• Amplitude affects how fast a wave travels. Amplitude relates to energy and loudness, not speed. Wave speed depends on the medium and the type of wave.
• Doubling the tension on a string doubles the wave speed. Because tension is under a square root, doubling it multiplies the speed by $\sqrt{2}$.
• Longitudinal waves can be polarized. Only transverse waves can be polarized, because polarization depends on a disturbance that is perpendicular to the direction of travel.
• Higher amplitude means higher frequency or pitch. Amplitude controls loudness and energy. Pitch is set by frequency, which is a separate property.

Practice Problem 1: Wave Speed on a String

Solution

To find the speed of a wave on a string, use the equation: $v_{\text{string}}=\sqrt{\frac{F_{T}}{m/\ell}}$

First, calculate the mass per unit length (linear density): $m/\ell = 0.05 \text{ kg} / 2.0 \text{ m} = 0.025 \text{ kg/m}$

Now substitute this value and the tension into the equation: $v_{\text{string}}=\sqrt{\frac{80 \text{ N}}{0.025 \text{ kg/m}}}$ $v_{\text{string}}=\sqrt{3200 \text{ m}^2/\text{s}^2}$ $v_{\text{string}}= 56.6 \text{ m/s}$

A wave pulse travels along this string at about 56.6 m/s.

Practice Problem 2: Comparing Wave Energy

Solution

The energy carried by a wave increases with increasing amplitude, and this relationship goes with the square of the amplitude: $E \propto A^2$

If wave A has twice the amplitude of wave B, then: $A_A = 2A_B$

The ratio of their energies is: $\frac{E_A}{E_B} = \frac{A_A^2}{A_B^2} = \frac{(2A_B)^2}{A_B^2} = \frac{4A_B^2}{A_B^2} = 4$

Wave A carries 4 times more energy than wave B. This shows why even a small increase in amplitude can lead to a large increase in the energy a wave carries.

Related AP Physics 2 Guides

• 14.2 Periodic Waves
• 14.3 Boundary Behavior of Waves and Polarization
• 14.6 Wave Interference and Standing Waves
• 14.7 Diffraction
• 14.4 Electromagnetic Waves
• 14.5 The Doppler Effect