WAVE - REVIEW

WAVES - PROPERTIES OF A WAVE #7

Energy Transport and the Amplitude of a Wave

• Remember, a wave is an energy transport phenomenon that transports energy along a medium without transporting matter. 
• A pulse or a wave is introduced into a slinky when a person holds the first coil and gives it a back-and-forth motion. This creates a disturbance within the medium; this disturbance subsequently travels from coil to coil, transporting energy as it moves. 
• The energy is imparted to the medium by the person as he/she does work upon the first coil to give it kinetic energy. This energy is transferred from coil to coil until it arrives at the end of the slinky. If you were holding the opposite end of the slinky, then you would feel the energy as it reaches your end. 
• In fact, a high energy pulse would likely do some rather noticeable work upon your hand upon reaching the end of the medium; the last coil of the medium would displace you hand in the same direction of motion of the coil. 
• For the same reasons, a high energy ocean wave can do considerable damage to the rocks and piers along the shoreline when it crashes upon it.

How is the Energy Transported Related to the Amplitude?

The amount of energy carried by a wave is related to the amplitude of the wave. 

• A high energy wave is characterized by a high amplitude; 
• A low energy wave is characterized by a low amplitude. 

Remember, the amplitude of a wave refers to the maximum amount of displacement of a particle on the medium from its rest position. 

Amplitude is the height of the wave. 

• The higher the amplitude, the higher the wave. Also, 
• The higher the amplitude the higher the energy of the wave. 

Can you see why? 

If the wave has a high amplitude, how must the particles in the wave be moving? A lot, or a little? If you said a lot you’re right! 

For a wave to have a high amplitude the particle has to be moving over a large distance (large being a relative term here, the distance may still be miniscule). The more the particle moves, the more work there is being done on the particle (work is force and distance). The more work there is, the more energy there is and so, a wave with a large amplitude has more energy then a wave with a small amplitude. If you've ever been in the ocean this may be more clear. Small little waves don’t have the energy to knock you over, but the larger ones...watch out! In sound, amplitude determines the loudness of the sound. In light, amplitude determines the brightness.

Consider two identical slinkies into which a pulse is introduced. If the same amount of energy is introduced into each slinky, then each pulse will have the same amplitude. But what if the slinkies are different? What if one is made of zinc and the other is made of copper? Will the amplitudes now be the same or different? If a pulse is introduced into two different slinkies by imparting the same amount of energy, then the amplitudes of the pulses will not necessarily be the same. In a situation such as this, the actual amplitude assumed by the pulse is dependent upon two types of factors: an inertial factor and an elastic factor. Two different materials have different mass densities. The imparting of energy to the first coil of a slinky is done by the application of a force to this coil. More massive slinkies have a greater inertia and thus tend to resist the force; this increased resistance by the greater mass tends to cause a reduction in the amplitude of the pulse. Different materials also have differing degrees of springiness or elasticity. A more elastic medium will tend to offer less resistance to the force and allow a greater amplitude pulse to travel through it; being less rigid (and therefore more elastic), the same force causes a greater amplitude.
 

 

WAVES - SOUND #2

A wave is a disturbance that moves along a medium from one end to the other. If one watches an ocean wave moving along the medium (the ocean water), one can observe that the crest of the wave is moving from one location to another over a given interval of time. The crest is observed to cover distance. 
The speed of an object refers to how fast an object is moving and is usually expressed as the distance traveled per time of travel. In the case of a wave, the speed is the distance traveled by a given point on the wave (such as a crest) in a given interval of time. In equation form,

• If the crest of an ocean wave moves a distance of 20 meters in 10 seconds,then the speed of the ocean wave is ???
  • 2.0 m/s

• On the other hand, if the crest of an ocean wave moves a distance of 20 meters in 10 seconds (the same amount of time), then the speed of this ocean wave is ???
  • 2.5 m/s.  
    The faster wave travels a greater distance in the same amount of time.

***Sometimes a wave encounters the end of a medium and the presence of a different medium. 

• For example, a wave introduced by a person into one end of a slinky will travel through the slinky and eventually reach the end of the slinky and the presence of the hand of a second person. 
  
  One behavior that waves undergo at the end of a medium is reflection. The wave will reflect or bounce off the person's hand. When a wave undergoes reflection, it remains within the medium and merely reverses its direction of travel. 
  

  • In the case of a slinky wave, the disturbance can be seen traveling back to the original end. A slinky wave that travels to the end of a slinky and back has doubled its distance. That is, by reflecting back to the original location, the wave has traveled a distance that is equal to twice the length of the slinky.

Reflection phenomena are commonly observed with sound waves. 

• When you let out a holler within a canyon, you often hear the echo of the holler. 
  
  The sound wave travels through the medium (air in this case), reflects off the canyon wall and returns to its origin (you). The result is that you hear the echo (the reflected sound wave) of your holler. A classic physics problem goes like this:

Noah stands 170 meters away from a steep canyon wall. He shouts and hears the echo of his voice one second later. What is the speed of the wave?

• In this instance, the sound wave travels 340 meters in 1 second, so the speed of the wave is 340 m/s. 
  
  
  Remember, when there is a reflection, the wave doubles its distance. In other words, the distance traveled by the sound wave in 1 second is equivalent to the 170 meters down to the canyon wall plus the 170 meters back from the canyon wall.

Variables Affecting Wave Speed - Think!!!!

What variables affect the speed at which a wave travels through a medium? 

Does the frequency or wavelength of the wave affect its speed? 

Does the amplitude of the wave affect its speed? 

Or are other variables such as the mass density of the medium or the elasticity of the medium responsible for affecting the speed of the wave? 

The speed of sound depends on the elasticity, density & temperature of medium
Elasticity - ability of a material to bounce back after being disturbed.

• rubber band is an elastic substance

sound travels more quickly in mediums that have a high degree of elasticity b/c when the particles are compressed, they quickly spread out again.  
Density – of a medium is how much matter, or mass, there is in a gvine amount of space, or volume.

• ·       Sound travel more slowly in dense metals.

Temperature – room temperature of about 20*C, sound travels at about 340 m/s. 

·         In a given medium, sound travel more slowly at lower temperatures & faster @ higher temperatures.

•  

  Factor	Change in Factor	Effect on Speed of Sound
  Elasticity	Increase in elasticity
  Density	Increase in density
  temperature	Decrease in temperature

  
  
   
  

Wave speed depends upon the medium through which the wave is moving. Only an alteration in the properties of the medium will cause a change in the speed.  

SPEED OF A WAVE - Check Your Understanding

Please add these questions with answers in your notebook.

1. A teacher attaches a slinky to the wall and begins introducing pulses with different amplitudes. Which of the two pulses (A or B) below will travel from the hand to the wall in the least amount of time? Justify your answer.

  
2. The teacher then begins introducing pulses with a different wavelength. Which of the two pulses (C or D) will travel from the hand to the wall in the least amount of time ? Justify your answer.

 
 
3. The time required for the sound waves (v = 340 m/s) to travel from the tuning fork to point A is ____ .

a. 0.020 second	b. 0.059 second
c. 0.59 second	d. 2.9 second

4. Two waves are traveling through the same container of nitrogen gas. Wave A has a wavelength of 1.5 m. Wave B has a wavelength of 4.5 m. The speed of wave B must be ________ the speed of wave A.

a. one-ninth	b. one-third
c. the same as	d. three times larger than

5. An automatic focus camera is able to focus on objects by use of an ultrasonic sound wave. The camera sends out sound waves that reflect off distant objects and return to the camera. A sensor detects the time it takes for the waves to return and then determines the distance an object is from the camera. The camera lens then focuses at that distance. Now that's a smart camera! In a subsequent life, you might have to be a camera; so try this problem for practice:

If a sound wave (speed = 340 m/s) returns to the camera 0.150 seconds after leaving the camera, then how far away is the object?

  6. TRUE or FALSE:

Doubling the frequency of a wave source doubles the speed of the waves.

7. While hiking through a canyon, Noah Formula lets out a scream. An echo (reflection of the scream off a nearby canyon wall) is heard 0.82 seconds after the scream. The speed of the sound wave in air is 342 m/s. Calculate the distance from Noah to the nearby canyon wall.

 8. Mac and Tosh are resting on top of the water near the end of the pool when Mac creates a surface wave. The wave travels the length of the pool and back in 25 seconds. The pool is 25 meters long. Determine the speed of the wave.
 
9. The water waves below are traveling along the surface of the ocean at a speed of 2.5 m/s and splashing periodically against Wilbert's perch. Each adjacent crest is 5 meters apart. The crests splash Wilbert's feet upon reaching his perch. How much time passes between each successive drenching? Answer and explain using complete sentences.

WAVES - TSUNAMI

Read on the following Web site about TSUNAMI.

READ on the following website about  TSUNAMI

TSUNAMI

WAVES - FREQUENCY & PERIOD OF A WAVE #6

In that lesson, it was mentioned that a wave is created in a slinky by the periodic and repeating vibration of the first coil of the slinky. This vibration creates a disturbance that moves through the slinky and transports energy from the first coil to the last coil. A single back-and-forth vibration of the first coil of a slinky introduces a pulse into the slinky. But the act of continually vibrating the first coil with a back-and-forth motion in periodic fashion introduces a wave into the slinky.

Suppose that a hand holding the first coil of a slinky is moved back-and-forth two complete cycles in one second. The rate of the hand's motion would be 2 cycles/second. The first coil, being attached to the hand, in turn would vibrate at a rate of 2 cycles/second. The second coil, being attached to the first coil, would vibrate at a rate of 2 cycles/second. The third coil, being attached to the second coil, would vibrate at a rate of 2 cycles/second. In fact, every coil of the slinky would vibrate at this rate of 2 cycles/second. This rate of 2 cycles/second is referred to as the frequency of the wave.

The frequency of a wave refers to how often the particles of the medium vibrate when a wave passes through the medium. Frequency is a part of our common, everyday language. For example, it is not uncommon to hear a question like "How frequently do you mow the lawn during the summer months?" Of course the question is an inquiry about how often the lawn is mowed and the answer is usually given in the form of "1 time per week." In mathematical terms, the frequency is the number of complete vibrational cycles of a medium per a given amount of time. Given this definition, it is reasonable that the quantity frequency would have units of cycles/second, waves/second, vibrations/second, or something/second. Another unit for frequency is the Hertz (abbreviated Hz) where 1 Hz is equivalent to 1 cycle/second. If a coil of slinky makes 2 vibrational cycles in one second, then the frequency is 2 Hz. If a coil of slinky makes 3 vibrational cycles in one second, then the frequency is 3 Hz. And if a coil makes 8 vibrational cycles in 4 seconds, then the frequency is 2 Hz (8 cycles/4 s = 2 cycles/s).

The quantity frequency is often confused with the quantity period.  Period refers to the time that it takes to do something. When an event occurs repeatedly, then we say that the event is periodic and refer to the time for the event to repeat itself as the period. The period of a wave is the time for a particle on a medium to make one complete vibrational cycle. Period, being a time, is measured in units of time such as seconds, hours, days or years. The period of orbit for the Earth around the Sun is approximately 365 days; it takes 365 days for the Earth to complete a cycle. The period of a typical class at a high school might be 55 minutes; every 55 minutes a class cycle begins (50 minutes for class and 5 minutes for passing time means that a class begins every 55 minutes). The period for the minute hand on a clock is 3600 seconds (60 minutes); it takes the minute hand 3600 seconds to complete one cycle around the clock.

Frequency and period are distinctly different, yet related, quantities. Frequency refers to how often something happens. Period refers to the time it takes something to happen.

• Frequency is a rate quantity. 
• Frequency is the cycles/second.
• Period is a time quantity. 
• Period is the seconds/cycle. 
• As an example of the distinction and the relatedness of frequency and period, consider a woodpecker that drums upon a tree at a periodic rate. If the woodpecker drums upon a tree 2 times in one second, then the frequency is 2 Hz. Each drum must endure for one-half a second, so the period is 0.5 s. If the woodpecker drums upon a tree 4 times in one second, then the frequency is 4 Hz; each drum must endure for one-fourth a second, so the period is 0.25 s. If the woodpecker drums upon a tree 5 times in one second, then the frequency is 5 Hz; each drum must endure for one-fifth a second, so the period is 0.2 s. Do you observe the relationship? Mathematically, the period is the reciprocal of the frequency and vice versa. In equation form, this is expressed as follows.

Since the symbol f is used for frequency and the symbol T is used for period, these equations are also expressed as:

The quantity frequency is also confused with the quantity speed. The speed of an object refers to how fast an object is moving and is usually expressed as the distance traveled per time of travel. For a wave, the speed is the distance traveled by a given point on the wave (such as a crest) in a given period of time. So while wave frequency refers to the number of cycles occurring per second, wave speed refers to the meters traveled per second. A wave can vibrate back and forth very frequently, yet have a small speed; and a wave can vibrate back and forth with a low frequency, yet have a high speed. Frequency and speed are distinctly different quantities. 

WAVES - ANATOMY #5

 transverse wave is a wave in which the particles of the medium are displaced in a direction perpendicular to the direction of energy transport. 

• A transverse wave can be created in a rope if the rope is stretched out horizontally and the end is vibrated back-and-forth in a vertical direction. If a snapshot of such a transverse wave could be taken so as to freeze the shape of the rope in time, then it would look like the following diagram.

The dashed line drawn through the center of the diagram represents the equilibrium or rest position of the string. This is the position that the string would assume if there were no disturbance moving through it. Once a disturbance is introduced into the string, the particles of the string begin to vibrate upwards and downwards. At any given moment in time, a particle on the medium could be above or below the rest position. Points A, E and H on the diagram represent the crests of this wave. 

The crest of a wave is the point on the medium that exhibits the maximum amount of positive or upward displacement from the rest position. Points C and J on the diagram represent the troughs of this wave. 

The trough of a wave is the point on the medium that exhibits the maximum amount of negative or downward displacement from the rest position.

The wave shown above can be described by a variety of properties. One such property is amplitude. The amplitude of a wave refers to the maximum amount of displacement of a particle on the medium from its rest position. In a sense, the amplitude is the distance from rest to crest. Similarly, the amplitude can be measured from the rest position to the trough position. In the diagram above, the amplitude could be measured as the distance of a line segment that is perpendicular to the rest position and extends vertically upward from the rest position to point A.

The wavelength is another property of a wave that is portrayed in the diagram above. The wavelength of a wave is simply the length of one complete wave cycle. If you were to trace your finger across the wave in the diagram above, you would notice that your finger repeats its path. A wave is a repeating pattern. It repeats itself in a periodic and regular fashion over both time and space. And the length of one such spatial repetition (known as a wave cycle) is the wavelength. The wavelength can be measured as the distance from crest to crest or from trough to trough. In fact, the wavelength of a wave can be measured as the distance from a point on a wave to the corresponding point on the next cycle of the wave. In the diagram above, the wavelength is the horizontal distance from A to E, or the horizontal distance from B to F, or the horizontal distance from D to G, or the horizontal distance from E to H. Any one of these distance measurements would suffice in determining the wavelength of this wave.

A longitudinal wave is a wave in which the particles of the medium are displaced in a direction parallel to the direction of energy transport. A longitudinal wave can be created in a slinky if the slinky is stretched out horizontally and the end coil is vibrated back-and-forth in a horizontal direction. If a snapshot of such a longitudinal wave could be taken so as to freeze the shape of the slinky in time, then it would look like the following diagram.

Because the coils of the slinky are vibrating longitudinally, there are regions where they become pressed together and other regions where they are spread apart. A region where the coils are pressed together in a small amount of space is known as a compression. A compression is a point on a medium through which a longitudinal wave is traveling that has the maximum density. A region where the coils are spread apart, thus maximizing the distance between coils, is known as a rarefaction. A rarefaction is a point on a medium through which a longitudinal wave is traveling that has the minimum density. Points A, C and E on the diagram above represent compressions and points B, D, and F represent rarefactions. While a transverse wave has an alternating pattern of crests and troughs, a longitudinal wave has an alternating pattern of compressions and rarefactions.

As discussed above, the wavelength of a wave is the length of one complete cycle of a wave. For a transverse wave, the wavelength is determined by measuring from crest to crest. A longitudinal wave does not have crest; so how can its wavelength be determined? The wavelength can always be determined by measuring the distance between any two corresponding points on adjacent waves. In the case of a longitudinal wave, a wavelength measurement is made by measuring the distance from a compression to the next compression or from a rarefaction to the next rarefaction. On the diagram above, the distance from point A to point C or from point B to point D would be representative of the wavelength.

 

Check Your Understanding

Consider the diagram below in order to answer questions #1-2.

1. The wavelength of the wave in the diagram above is given by letter ______.

2. The amplitude of the wave in the diagram above is given by letter _____.

3. Indicate the interval that represents one full wavelength.

a. A to C

b. B to D

c. A to G

d. C to G

**********************************************************





1)   Answer: A
The wavelength is the distance from crest to crest (or from trough to trough) (or between any two corresponding points on adjacent waves).

 2)   Answer: D
The amplitude is the distance from rest to crest or from rest to trough.

3)Answer: D
The wavelength is the distance from crest to crest, trough to trough, or from a point on one wave cycle to the corresponding point on the next adjacent wave cycle.

The nature of a wave was discussed in Lesson 1 of this unit. In that lesson, it was mentioned that a wave is created in a slinky by the periodic and repeating vibration of the first coil of the slinky. This vibration creates a disturbance that moves through the slinky and transports energy from the first coil to the last coil. A single back-and-forth vibration of the first coil of a slinky introduces a pulse into the slinky. But the act of continually vibrating the first coil with a back-and-forth motion in periodic fashion introduces a wave into the slinky.

Suppose that a hand holding the first coil of a slinky is moved back-and-forth two complete cycles in one second. The rate of the hand's motion would be 2 cycles/second. The first coil, being attached to the hand, in turn would vibrate at a rate of 2 cycles/second. The second coil, being attached to the first coil, would vibrate at a rate of 2 cycles/second. The third coil, being attached to the second coil, would vibrate at a rate of 2 cycles/second. In fact, every coil of the slinky would vibrate at this rate of 2 cycles/second. This rate of 2 cycles/second is referred to as the frequency of the wave. The frequency of a wave refers to how often the particles of the medium vibrate when a wave passes through the medium. Frequency is a part of our common, everyday language. For example, it is not uncommon to hear a question like "How frequently do you mow the lawn during the summer months?" Of course the question is an inquiry about how often the lawn is mowed and the answer is usually given in the form of "1 time per week." In mathematical terms, the frequency is the number of complete vibrational cycles of a medium per a given amount of time. Given this definition, it is reasonable that the quantity frequencywould have units of cycles/second, waves/second, vibrations/second, or something/second. Another unit for frequency is the Hertz (abbreviated Hz) where 1 Hz is equivalent to 1 cycle/second. If a coil of slinky makes 2 vibrational cycles in one second, then the frequency is 2 Hz. If a coil of slinky makes 3 vibrational cycles in one second, then the frequency is 3 Hz. And if a coil makes 8 vibrational cycles in 4 seconds, then the frequency is 2 Hz (8 cycles/4 s = 2 cycles/s).

The quantity frequency is often confused with the quantity period. Period refers to the time that it takes to do something. When an event occurs repeatedly, then we say that the event is periodic and refer to the time for the event to repeat itself as the period. The period of a wave is the time for a particle on a medium to make one complete vibrational cycle. Period, being a time, is measured in units of time such as seconds, hours, days or years. The period of orbit for the Earth around the Sun is approximately 365 days; it takes 365 days for the Earth to complete a cycle. The period of a typical class at a high school might be 55 minutes; every 55 minutes a class cycle begins (50 minutes for class and 5 minutes for passing time means that a class begins every 55 minutes). The period for the minute hand on a clock is 3600 seconds (60 minutes); it takes the minute hand 3600 seconds to complete one cycle around the clock.

Frequency and period are distinctly different, yet related, quantities. Frequency refers to how often something happens. Period refers to the time it takes something to happen. Frequency is a rate quantity. Period is a time quantity. Frequency is the cycles/second. Period is the seconds/cycle. As an example of the distinction and the relatedness of frequency and period, consider a woodpecker that drums upon a tree at a periodic rate. If the woodpecker drums upon a tree 2 times in one second, then the frequency is 2 Hz. Each drum must endure for one-half a second, so the period is 0.5 s. If the woodpecker drums upon a tree 4 times in one second, then the frequency is 4 Hz; each drum must endure for one-fourth a second, so the period is 0.25 s. If the woodpecker drums upon a tree 5 times in one second, then the frequency is 5 Hz; each drum must endure for one-fifth a second, so the period is 0.2 s. Do you observe the relationship? Mathematically, the period is the reciprocal of the frequency and vice versa. In equation form, this is expressed as follows.

Since the symbol f is used for frequency and the symbol T is used for period, these equations are also expressed as:

The quantity frequency is also confused with the quantity speed. The speed of an object refers to how fast an object is moving and is usually expressed as the distance traveled per time of travel. For a wave, the speed is the distance traveled by a given point on the wave (such as a crest) in a given period of time. So while wave frequency refers to the number of cycles occurring per second, wave speed refers to the meters traveled per second. A wave can vibrate back and forth very frequently, yet have a small speed; and a wave can vibrate back and forth with a low frequency, yet have a high speed. Frequency and speed are distinctly different quantities. Wave speed will be discussed in more detail later in this lesson.

Investigate!

How do changes in the frequency of a wave affect the wavelength of a wave? Use the Wave plotter widget below to find out. Alter the frequency and observe how the pattern changes.

	Wave Plotter
	Enter a value for amplitude and select a frequency. Then click the Plot the Wave button to view the result. Amplitude (m): Frequency (Hz): mediumlowvery lowhighvery high NOTE: The on-screen height of the wave is the same each time; yet the vertical axis is scaled differently. Plot the Wave

 

Check Your Understanding

Throughout this unit, internalize the meaning of terms such as period, frequency, and wavelength. Utilize the meaning of these terms to answer conceptual questions; avoid a formula fixation.

1. A wave is introduced into a thin wire held tight at each end. It has an amplitude of 3.8 cm, a frequency of 51.2 Hz and a distance from a crest to the neighboring trough of 12.8 cm. Determine the period of such a wave.