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Waves

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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.

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Assessment 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. What is the frequency? What is the wavelength? What is the amplitude? Calculate the wave speed.

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Assessment Provide an example of a transverse wave and a longitudinal wave. Describe how they are similar and how they are different. Describe, in your own words, how a sound speaker moves to create sound waves.

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**Physics terms oscillation wave wavelength frequency amplitude**

transverse wave longitudinal wave polarization

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Equations Wave velocity equals the frequency multiplied by the wavelength.

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**What is a wave? 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.

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Waves and energy Waves are an essential way in which energy travels from one place to another. Waves propagate through space, spreading energy out to other regions which may be quite far away.

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Waves in time and space A wave oscillates up and down over time at a given point in space.

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Waves in time and space A wave oscillates up and down over time at a given point in space. The wave’s oscillations extend in space at any instant in time.

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Exploring the ideas In Investigation 15 A you will explore the wave properties of amplitude, wavelength, and frequency. Click to open the interactive simulation.

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**Investigation Part 1: Match a wave’s properties**

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.

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**Investigation Part 1: Match a wave’s properties**

Open the simulation. You will create a model of a wave (red line) to match the blue waves. Adjust amplitude and wavelength to match the blue wave. Run and Pause the waves. Adjust the frequency until the bobbing red circle matches the bobbing of the floating ball.

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**Investigation Questions for Part 1**

Describe how changing the amplitude changes the wave. Describe the effect of changing the wavelength. Describe the effect of changing the frequency. What are the frequency, amplitude, and wavelength of the blue wave?

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**Investigation Questions for Part 1**

Draw a graph showing the amplitude and wavelength of this wave. Calculate the speed of the wave. How does your calculated speed agree with the observed movement of the wave fronts across the screen?

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**Investigation Part 2: Transverse and longitudinal waves**

Hold one end of a long spring and have your partner hold the other end. Stretch the spring so it is not slack. Create transverse waves by moving your hand side-to-side. Create longitudinal waves by moving your hand sharply towards your partner. Repeat using a wave motion rope or other heavy string.

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**Investigation Questions for Part 2**

What are the differences between these two types of waves? Describe the characteristics of each in words. Can you make both types of waves on both pieces of equipment? Why or why not? Can you create waves of different velocities with the spring or rope? If so, how?

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Amplitude The amplitude A of a wave is the maximum amount the water rises or falls compared to its average resting level. The amplitude of different types of waves may have different units: A Water wave amplitude is a distance, in meters. Sound wave amplitude is a pressure, in pascals.

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Wavelength λ 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?

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Frequency The frequency f of a wave is a measure of how quickly it oscillates. The unit for frequency is the hertz, or Hz. One hertz equals one cycle per second.

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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?

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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? 2 Hz

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**Frequency 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.

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Wave speed 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)

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Wave speed As a wave moves forward, it advances one wavelength with each complete cycle. distance:

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Wave speed As a wave moves forward, it advances one wavelength with each complete cycle. distance: speed:

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Wave speed As a wave moves forward, it advances one wavelength with each complete cycle. distance: speed: frequency:

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Wave speed As a wave moves forward, it advances one wavelength with each complete cycle. distance: speed: frequency: wave speed:

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Exploring the ideas Click on this calculator on page 413

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**Engaging with the concepts**

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

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**Engaging with the concepts**

A water wave has a speed of 5.0 m/s and a wavelength of 2.0 m. What is its frequency? hertz Find two different ways to get a speed of 100 m/s. Frequency 5.0 2.5 2.0

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**Engaging with the concepts**

A water wave has a speed of 5.0 m/s and a wavelength of 2.0 m. What is its frequency? hertz Find two different ways to get a speed of 100 m/s. Speed of wave 100 25 4.0 There are many correct answers!

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**Engaging with the concepts**

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? Wavelength 343 686

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**Engaging with the concepts**

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? λ = 50 cm What happens if frequency is doubled? Wavelength 343 686 0.50 Increase the volume. What wave characteristic is affected?

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**Engaging with the concepts**

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? λ = 50 cm What happens if frequency is doubled? Pitch increases and wavelength is halved. Wavelength 343 1372 0.25 Increase the volume. What wave characteristic is affected? the amplitude

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Test your knowledge This wave’s motion is graphed as a function of time and distance. What is the wave frequency? What is the wavelength? What is the amplitude? Calculate the speed of the wave.

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Test your knowledge This wave’s motion is graphed as a function of time and distance. What is the wave frequency? 1 Hz What is the wavelength? 5 cm What is the amplitude? cm Calculate the speed of the wave. 5 cm/s (0.05 m/s)

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Test your knowledge Two 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? Asked: speed v Given: Relationship: Solution:

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Test your knowledge Two 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? Asked: speed v Given: Relationship: Solution:

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**Wave energy 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.

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**Energy and frequency The energy of a wave increases with frequency:**

lower energy low frequency (slower oscillations) long wavelength

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**Energy and frequency The energy of a wave increases with frequency:**

lower energy higher energy low frequency high frequency (slower oscillations) (faster oscillations) long wavelength short wavelength

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Energy and amplitude The energy of a wave also increases with amplitude: lower energy small amplitude

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Energy and amplitude The energy of a wave also increases with amplitude: lower energy higher energy small amplitude large amplitude

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**Energy and amplitude As a wave spreads out, its amplitude decreases.**

One reason is damping; friction reduces the wave’s energy over time.

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**Energy and 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.

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

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Test your knowledge Although speech gets quieter farther from its source, the words and tone stay the same. Why? As the wave spreads out the 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.

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**Waves in 3-D space Waves can cause oscillations in three dimensions.**

The direction of motion of the wave is defined as the forward dimension. The other two dimensions (left-right and up-down) are perpendicular to the direction of motion.

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Transverse waves A transverse wave causes oscillations that are perpendicular to the forward motion of the wave. Examples: waves in a string light waves

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Transverse waves Transverse waves can oscillate in any direction that is perpendicular to the direction the wave is traveling! Try creating both vertically and horizontally oscillating transverse waves using a wave motion rope.

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Longitudinal 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 Move a Slinky® rapidly forward and back to create a longitudinal compression wave.

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Longitudinal waves Point out that amplitude for this wave is not a distance. it is the coil density. Show the students that the wave crests and troughs on the graph correspond to points of most and least coils per centimeter in the Slinky® illustration.

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**Polarization Polarization describes the direction of**

the oscillation in a plane perpendicular to the wave velocity. The wave in this figure is polarized. It is traveling in the z-direction and its oscillations occur only in the y-direction—not in the x-direction.

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Polarization What kind of waves can be polarized? Transverse waves? longitudinal waves? or both types?

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Polarization What kind of waves can be polarized? Transverse waves? longitudinal waves? or both types? Transverse waves, such as light waves, can be polarized. Longitudinal waves, such as sound waves, cannot be polarized.

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Assessment 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. What is the frequency? What is the wavelength? What is the amplitude? Calculate the wave speed.

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Assessment 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. What is the frequency? 0.5 Hz What is the wavelength? 20 cm What is the amplitude? 0.5 cm Calculate the wave speed.

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

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Assessment 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.

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

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Assessment 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.

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