WavesPg. 39

Objectives• Investigate and analyze

the characteristics of waves including: velocity, frequency, amplitude, and wavelength.

• Compare the characteristics and behaviors of transverse waves and longitudinal waves.

Physics terms• oscillation

• wave

• wavelength

• frequency

• Amplitude

• transverse wave

• longitudinal wave

• polarization

Equations

Wave velocity equals the frequency multiplied by the wavelength.

Equations

The period of an oscillator is the time to complete one cycle.

The frequency of an oscillator is the inverse of its period.

Oscillators

An oscillator is a system with motion that repeats in cycles.

Drop a pebble on a pond on a calm day.

As the pebble breaks the surface, the water oscillates up and down—in harmonic motion.

Ripples form and spread out.

An oscillation that travels is a wave.

What is a wave?

Waves are an essential way in which energy travels from one place to another.

Waves move through space, spreading energy out to other regions which may be quite far away.

Waves and energy

Click to open the interactive simulation.

Exploring the ideasIn Investigation 15 A you will explore the wave properties of amplitude, wavelength, and frequency.

http://www.essential-physics.com/TX/sbookStudent ID login: 742  379  6973-Click on the “investigation” icon-Scroll down & click on Investigation 15A- Match a wave’s properties-Select the investigation icon-Complete simulation & answer ?’s a-e

This simulation allows you to overlay a mathematical model of a wave on a plotted blue wave representing water.

When you match the wave’s characteristics, your mathematical wave model will move with the blue wave.

InvestigationPart 1: Match a wave’s properties

1. Open the simulation. You will create a model of a wave (red line) to match the blue waves.

2. Adjust amplitude and wavelength to match the blue wave.

3. Run and Pause the waves. Adjust the frequency until the bobbing red circle matches the bobbing of the floating ball.

InvestigationPart 1: Match a wave’s properties

a. Describe how changing the amplitude changes the wave.

b. Describe the effect of changing the wavelength.

c. Describe the effect of changing the frequency.

d. What are the frequency, amplitude, and wavelength of the blue wave?

InvestigationPart 1 Post-Simulation Analysis Questions

e. Calculate the speed of the wave. How does your calculated speed agree with the observed movement of the wave fronts across the screen?

InvestigationPart 1 Post-Simulation Analysis Questions

1. Hold one end of a long spring and have your partner hold the other end. Stretch the spring so it is not slack.

2. Create transverse waves by moving your hand side-to-side.

3. Create longitudinal waves by moving your hand sharply towards your partner.

4. Repeat using a wave motion rope or other heavy string.

InvestigationPart 2: Transverse and longitudinal waves

a. What are the differences between these two types of waves? Describe the characteristics of each in words.

b. Can you make both types of waves on both pieces of equipment? Why or why not?

c. Can you create waves of different velocities with the spring or rope? If so, how?

InvestigationPost Simulation Analysis Questions for Part 2

PeriodA full cycle is one complete back and forth motion.

The period is the time it takes to complete one full cycle.

Period T is measured in seconds.

T

PeriodWhat is the period of the following oscillators?

1. Earth in its rotation

2. your heartbeat

3. the minute hand on a clock

4. a classroom pendulum

1 day, or 24 hours, or 86,400 seconds

about 1 second

1 hour

typically 1-2 seconds

A

The amplitude A of a wave is the maximum amount the wave rises or falls compared to its average resting level.

The amplitude of different types of waves may have different units:

• Water wave amplitude is a distance, in meters. • Sound wave amplitude is a pressure, in pascals.

Amplitude

The wavelength λ is the distance a wave travels before it begins to repeat itself.

The wavelength can be measured from peak to peak, or trough to trough. How many wavelengths

appear in this figure?

Wavelength

λ

FrequencyFrequency is how many cycles are completed each second.

Frequency f is measured in hertz, or Hz.

FrequencyWhat is the frequency of these oscillators?

1.your heartbeat

2.a fan that rotates 360 times a minute

3.the vibration of a guitar string

1 – 2 beats per second, or 1 – 2 Hz

6 cycles per second, or 6 Hz

100 – 800 Hz

The frequency f of a wave is a measure of how quickly it oscillates.

One hertz equals one cycle per second.

Frequency

When a wave has a frequency of 10 Hz = 10 cycles/second, then 10 waves travel past a given point each second.

What is the frequency of the wave shown below?

Frequency

2 Hz

The frequency of a wave conveys information.

Frequency remains the same even if the wave amplitude decreases as it spreads out.

• the frequency of a light wave determines its color.• the frequency of a sound wave determines its pitch.

Frequency

The speed of a wave depends on the type of wave and on its medium.

Examples:• speed of typical water waves: 5 m/s

• speed of sound in air: 343 m/s

• speed of light: 300,000,000 m/s (in a vacuum)

Wave speed

As a wave moves forward, it advances one wavelength with each complete cycle.

distance:

speed:

frequency:

wave speed:

Wave speed

Click on this calculatoron page 413

Exploring the ideashttp://www.essential-physics.com/TX/sbookStudent ID login: 742  379  6973-Click on the “interactive” icon-Scroll down & find Ch.15 Waves- Interactive Calculators-Click on Speed, Wavelength & frequency of a wave-Select the calculator icon-Use the interactive calculator to solve the problems

A water wave has a speed of 5.0 m/s and a wavelength of 2.0 m. What is its frequency?

Find two different ways to get a speed of 100 m/s.

Engaging with the concepts

Frequency

5.0 2.02.5

2.5 hertz

A sound wave has a speed of 343 m/s in air. What is the wavelength of a sound wave with frequency of 686 Hz?

What happens if frequency is doubled?

Increase the volume. What wave characteristic is affected?

Engaging with the concepts

λ = 50 cm

Pitch increases and wavelength is halved.

the amplitude

Test your knowledge

This wave’s motion is graphed as a function of time and distance.

a. What is the wave frequency?

b. What is the wavelength?

c. What is the amplitude?

d. Calculate the speed of the wave.

This wave’s motion is graphed as a function of time and distance.

a. What is the wave frequency? 1 Hzb. What is the wavelength? 5 cmc. What is the amplitude? 10 cmd. Calculate the speed of the wave. 5 cm/s (0.05 m/s)

Test your knowledge

Test your knowledgeTwo students use a 10-meter-long spring to create a standing wave. The wavelength is 2.0 m and the frequency is 2.0 Hz.

How fast is the wave traveling along the spring?

Given(s):

Unknown:

Equation:

Sub:

Solution:

speed v

A wave is an organized mechanism for transferring energy.

• As a wave moves through matter, its energy causes the matter to respond.

• After the wave passes, the matter returns to equilibrium.

Wave energy

lower energyhigher energy

low frequencyhigh frequency

(slower oscillations)(faster oscillations)

long wavelength short wavelength

The energy of a wave increases with frequency:

Energy and frequency

lower energy higher energy

small amplitudelarge amplitude

Energy and amplitudeThe energy of a wave also increases with amplitude:

As a wave spreads out, its amplitude decreases. • One reason is damping;

friction reduces the wave’s energy over time.

• Another reason is that as the wave propagates outward, its energy is spread over a larger area.

Energy and amplitude

Amplitude of the sound waves is reduced, but the frequency remains constant.

The waves still transfer the same information, even though they have less energy.

Test your knowledgeAlthough speech gets quieter farther from its source, the words and tone stay the same. Why?

Transverse waves can oscillate in any direction that is perpendicular to the direction the wave is traveling!

Transverse wavesA transverse wave causes oscillations that are perpendicular to the forward motion of the wave.

Examples:• waves in a string• light waves

A longitudinal wave causes oscillations that move back and forth in the same direction as the traveling wave.

Examples:• sound waves• the waves in a spring as

shown in this figure

Longitudinal waves

Longitudinal waves

1. Determine the amplitude, period, and frequency from the graph.

Assessment

Assessment

A = 7.5 cm

Assessment

T = 8 seconds

Assessment

f = 0.12 Hz

f 1

T

1

8 s0.12 Hz

Assessment2. These graphs show the oscillation of a point on a wave as a function of time, and the oscillation of the extended wave in space at a moment in time.

a. What is the frequency?

b. What is the wavelength?

c. What is the amplitude?

d. Calculate the wave speed.

Assessment2. These graphs show the oscillation of a point on a wave as a function of time, and the oscillation of the extended wave in space at a moment in time.

a. What is the frequency? 0.5 Hz

b. What is the wavelength? 20 cm

c. What is the amplitude? 0.5 cm

d. Calculate the wave speed.

3. Provide an example of a transverse wave and a longitudinal wave. Describe how they are similar and how they are different.

Assessment

3. Provide an example of a transverse wave and a longitudinal wave. Describe how they are similar and how they are different.

Each wave is an oscillation that transfers energy.

Waves in a string are transverse waves. Each segment of the string oscillates perpendicular to the forward motion of the wave.

Sound is a longitudinal wave. The air molecules oscillate back and forth, parallel to the direction of the wave’s forward motion.

Assessment

4. Describe, in your own words, how a sound speaker moves to create sound waves.

Assessment

4. Describe, in your own words, how a sound speaker moves to create sound waves.

A sound speaker oscillates back and forth to create sound waves, which are longitudinal compression waves.

Assessment