# measuring waves

## kqed science of big waves

The organizers of the famous Maverick surf contest have voted that the conditions are right for hanging ten this weekend. The monster waves at Mavericks attract big wave surfers from around the world. But what exactly makes these Half Moon Bay waves so big? For more information on waves, see http://science.kqed.org/quest/video/scie MEDIA Click image to the left or use the URL below. URL:

## wave frequency

The number of waves that pass a fixed point in a given amount of time is wave frequency. Wave frequency can be measured by counting the number of crests or compressions that pass the point in 1 second or other time period. The higher the number is, the greater is the frequency of the wave. The SI unit for wave frequency is the hertz (Hz), where 1 hertz equals 1 wave passing a fixed point in 1 second. Figure 19.13 shows high-frequency and low- frequency transverse waves. You can simulate transverse waves with different frequencies at this URL: http://zonal The frequency of a wave is the same as the frequency of the vibrations that caused the wave. For example, to generate a higher-frequency wave in a rope, you must move the rope up and down more quickly. This takes more energy, so a higher-frequency wave has more energy than a lower-frequency wave with the same amplitude.

## wave frequency and speed

Imagine making transverse waves in a rope, like the waves in Figure 19.2. You tie one end of the rope to a doorknob or other fixed point and move the other end up and down with your hand. You can move the rope up and down slowly or quickly. How quickly you move the rope determines the frequency of the waves.

## the medium matters

The speed of most waves depends on the medium through which they are traveling. Generally, waves travel fastest through solids and slowest through gases. Thats because particles are closest together in solids and farthest apart in gases. When particles are farther apart, it takes longer for the energy of the disturbance to pass from particle to particle.

## wave speed

Assume that you move one end of a rope up and down just once. How long will take the wave to travel down the rope to the other end? This depends on the speed of the wave. Wave speed is how far the wave travels in a given amount of time, such as how many meters it travels per second. Wave speed is not the same thing as wave frequency, but it is related to frequency and also to wavelength. This equation shows how the three factors are related: Speed = Wavelength Frequency In this equation, wavelength is measured in meters and frequency is measured in hertz, or number of waves per second. Therefore, wave speed is given in meters per second. The equation for wave speed can be used to calculate the speed of a wave when both wavelength and wave frequency are known. Consider an ocean wave with a wavelength of 3 meters and a frequency of 1 hertz. The speed of the wave is: Speed = 3 m 1 wave/s = 3 m/s You Try It! Problem: Jera made a wave in a spring by pushing and pulling on one end. The wavelength is 0.1 m, and the wave frequency is 0.2 m/s. What is the speed of the wave? If you want more practice calculating wave speed from wavelength and frequency, try the problems at this URL: http The equation for wave speed (above) can be rewritten as: Frequency = Speed Speed or Wavelength = Wavelength Frequency Therefore, if you know the speed of a wave and either the wavelength or wave frequency, you can calculate the missing value. For example, suppose that a wave is traveling at a speed of 2 meters per second and has a wavelength of 1 meter. Then the frequency of the wave is: Frequency = 2 m/s = 2 waves/s, or 2 Hz 1m You Try It! Problem: A wave is traveling at a speed of 2 m/s and has a frequency of 2 Hz. What is its wavelength?

## wave amplitude and wavelength

The height of a wave is its amplitude. Another measure of wave size is wavelength. Both wave amplitude and wave- length are described in detail below. Figure 19.11 shows these wave measures for both transverse and longitudinal waves. You can also simulate waves with different amplitudes and wavelengths by doing the interactive animation at this URL: http://sci-culture.com/advancedpoll/GCSE/sine%20wave%20simulator.html .

## wavelength

Another important measure of wave size is wavelength. Wavelength is the distance between two corresponding points on adjacent waves (see Figure 19.11). Wavelength can be measured as the distance between two adjacent crests of a transverse wave or two adjacent compressions of a longitudinal wave. It is usually measured in meters. Wavelength is related to the energy of a wave. Short-wavelength waves have more energy than long-wavelength waves of the same amplitude. You can see examples of waves with shorter and longer wavelengths in Figure 19.12.

## wave amplitude

Wave amplitude is the maximum distance the particles of a medium move from their resting position when a wave passes through. The resting position is where the particles would be in the absence of a wave. In a transverse wave, wave amplitude is the height of each crest above the resting position. The higher the crests are, the greater the amplitude. In a longitudinal wave, amplitude is a measure of how compressed particles of the medium become when the wave passes through. The closer together the particles are, the greater the amplitude. What determines a waves amplitude? It depends on the energy of the disturbance that causes the wave. A wave caused by a disturbance with more energy has greater amplitude. Imagine dropping a small pebble into a pond of still water. Tiny ripples will move out from the disturbance in concentric circles, like those in Figure 19.1. The ripples are low-amplitude waves. Now imagine throwing a big boulder into the pond. Very large waves will be generated by the disturbance. These waves are high-amplitude waves.

## instructional diagrams

The figure shows a transverse wave. In a transverse wave, wave amplitude is the height of each crest above the resting position. The higher the crests are, the greater the amplitude. Another important measure of wave size is wavelength. Wave amplitude is the maximum distance the particles of a medium move from their resting position when a wave passes through. The resting position (dotted line in the middle of the wave) is where the particles would be in the absence of a wave. Wavelength can be measured as the distance between two adjacent crests of a transverse wave. It is usually measured in meters. Wavelength is related to the energy of a wave. Short-wavelength waves have more energy than long-wavelength waves of the same amplitude.

This diagram represents a sound wave and its characteristics. The peak of a wave is called compression or crest. The valley of a wave is called rarefaction or trough. Wave length is the length between two consecutive peaks, i.e. crest or two consecutive valleys, i.e. trough of a wave. Louder sound has shorter wavelength and softer sound has longer wavelength. Magnitude of maximum disturbance on either side of the normal position or mean value in a medium is called amplitude. In other words, amplitude is the distance from normal to the crest or trough. Time required to produce one complete wave is called time period or time taken to complete on oscillation is called the time period of the sound wave. The number of sound waves produced in unit time is called the frequency of sound waves. Frequency is the reciprocal of the time period of wave. Distance covered by sound wave in unit time is called the velocity of sound wave.

## questions

The less compressed particles of matter become in a longitudinal wave, the greater the waves amplitude.

``````a. true

-->  b. false
``````

In a longitudinal wave, amplitude is a measure of

``````a. how many waves pass a fixed point each second.

-->  b. how close together particles of the medium become.

c. how quickly the wave travels a given distance.

d. how far apart adjacent compressions are.
``````

The distance between two adjacent compressions of a longitudinal wave is its wavelength.

``````-->  a. true

b. false
``````

If two waves have the same amplitude, the wave with more energy is the wave with the

``````-->  a. shorter wavelength.

b. lower frequency.

c. denser medium.

d. slower spee
``````

The frequency of a wave is the same as the frequency of the vibrations that caused the wave.

``````-->  a. true

b. false
``````

If two waves have the same speed, the wave with a higher frequency must have a

``````-->  a. shorter wavelength.

b. longer wavelength.

c. greater amplitude.

d. two of the above
``````

Wave speed is a product of

``````-->  a. wavelength and frequency.

b. wavelength and amplitude.

c. frequency and amplitude.

d. none of the above
``````

Wave speed measures the same thing as wave frequency.

``````a. true

-->  b. false
``````

Wavelength equals wave speed multiplied by wave frequency.

``````a. true

-->  b. false
``````

What is the frequency of a wave that has a wavelength of 2 m and a speed of 2 m/s?

``````a. 4 Hz

b. 2 Hz

-->  c. 1 Hz

d. 12 Hz
``````

The resting position of particles in a longitudinal wave is where the particles are most spread out.

``````a. true

-->  b. false
``````

A wave caused by a disturbance with greater energy has greater amplitude.

``````-->  a. true

b. false
``````

If you know the speed and wavelength of a wave, you can calculate its frequency.

``````-->  a. true

b. false
``````

Waves generally travel most slowly in gases.

``````-->  a. true

b. false
``````

A wave with a higher frequency always has a greater speed than a wave with a lower frequency.

``````a. true

-->  b. false
``````

One measure of wave size is wave frequency.

``````a. true

-->  b. false
``````

Measures of wave size include

``````a. wavelength.

b. wave amplitude.

c. wave frequency.

-->  d. two of the above
``````

The resting position of a transverse wave is called a trough.

``````a. true

-->  b. false
``````

The amplitude of a transverse wave is the distance between

``````a. two adjacent crests.

b. two adjacent troughs.

c. a crest and a trough.

-->  d. a crest and the resting position.
``````

What is the speed of a wave that has a wavelength of 0.5 meters and a frequency of 2 waves per second?

``````a. 14 m/s

-->  b. 1 m/s

c. 4 m/s

d. 10 m/s
``````

If you know only a waves amplitude and wavelength, you can calculate its speed.

``````a. true

-->  b. false
``````

Wave amplitude depends on

``````a. wavelength.

b. wave speed.

-->  c. wave energy.

d. wave frequency.

e. wave energy of the original disturbanc
``````

Wave speed and wavelength have an inverse relationship.

``````a. true

-->  b. false
``````

A tsunami is an ocean wave with an unusually great amplitude.

``````-->  a. true

b. false
``````

When one wave passes a fixed point every second, the frequency of the waves is

``````a. 0.1 Hz.

-->  b. 1 Hz.

c. 10 Hz.

d. none of the above
``````

Assume that a wave has a fixed speed. If the frequency of the wave increases, its wavelength

``````a. increases.

-->  b. decreases.

c. does not change.

d. may or may not change.
``````

The speed of waves depends on their

``````a. wavelength.

b. frequency.

c. medium.

-->  d. all of the above
``````

maximum distance the particles of a medium move from their resting position

``````a. hertz

b. wavelength

-->  c. wave amplitude

d. resting position

e. wave frequency

f. crest

g. wave speed
``````

number of waves that pass a fixed point in a given amount of time

``````a. hertz

b. wavelength

c. wave amplitude

d. resting position

-->  e. wave frequency

f. crest

g. wave speed
``````

how far a wave travels in a given amount of time

``````a. hertz

b. wavelength

c. wave amplitude

d. resting position

e. wave frequency

f. crest

-->  g. wave speed
``````

highest point reached by particles of the medium in a transverse wave

``````a. hertz

b. wavelength

c. wave amplitude

d. resting position

e. wave frequency

-->  f. crest

g. wave speed
``````

distance between two corresponding points on adjacent waves

``````a. hertz

-->  b. wavelength

c. wave amplitude

d. resting position

e. wave frequency

f. crest

g. wave speed
``````

location of particles of the medium in the absence of a wave

``````a. hertz

b. wavelength

c. wave amplitude

-->  d. resting position

e. wave frequency

f. crest

g. wave speed
``````

SI unit for wave frequency

``````-->  a. hertz

b. wavelength

c. wave amplitude

d. resting position

e. wave frequency

f. crest

g. wave speed
``````

## diagram questions

Which label shows the wavelength of this wave?

``````-->  a. T

b. D

c. N

d. M
``````

By what letter is the crest represented in the diagram?

``````a. L

-->  b. H

c. S

d. W
``````

Which label refers to the trough?

``````a. L

b. S

-->  c. K

d. H
``````

What do you call letters W, S and L?

``````-->  a. PERIOD

b. DOUBLE PERIOD

c. AMPLITUDE

d. HALF PERIOD
``````

Select a period in the diagram.

``````-->  a. S

b. W, S AND L

c. K OR H

d. W AND L
``````

Which label depicts the crest?

``````a. E

b. V

-->  c. T

d. N
``````

Which letter corresponds to the measurement from the equilibrium point to the crest point?

``````a. X

-->  b. S

c. IT IS NOT SHOWN.

d. CANNOT BE DETERMINED.
``````

By what letter is the wave crest represented in the diagram?

``````a. S

b. U

-->  c. N

d. R
``````

Identify one wave period.

``````a. H

b. S

-->  c. R

d. U
``````

Trough means low, where is the wave trough in this picture?

``````a. N

-->  b. K

c. S

d. R
``````

By what letter is the elevation represented in the diagram?

``````a. P

-->  b. E

c. F

d. V
``````

Which label shows the amplitude of the wave?

``````-->  a. P

b. V

c. E

d. F
``````

What is P in this image of waves?

``````a. WAVELENGTH

-->  b. AMPLITUDE

c. CREST

d. TROUGH
``````

Which letter represents a crest?

``````a. P

b. V

-->  c. F

d. E
``````

What is the highest point of the wave called?

``````a. length

b. amplitude

c. trough

-->  d. crest
``````

If the bottom of the wave is called a trough, then what is the top of the wave called?

``````a. trough

b. dashed line

c. orange line

-->  d. crest
``````

How many crests are on that wave?

``````a. 3

b. 4

-->  c. 2

d. 1
``````

How many wavelengths are pictured?

``````a. 4

b. 3

c. 2

-->  d. 1
``````

What would happen to if the crests are further apart?

``````a. It would become smaller

b. It would stay the same

-->  c. It would become bigger

d. It would become zero
``````

What does the letter a represent?

``````-->  a. amplitide

b. high frequency

c. low frequency

d. wavelength
``````

How many crests can be seen in the diagram?

``````a. 1

-->  b. 2

c. 3

d. 4
``````

What is the part above the center of the wave called?

``````a. Equator

b. Trough

-->  c. Crest

d. Wavelength
``````

Which label identify the height of a wave?

``````a. Crest

-->  b. Amplitude

c. Wave length

d. Trough
``````

How many wave lengths are depicted in the diagram?

``````a. 2

b. 5

-->  c. 4

d. 6
``````

Which of the following shows the distance between two adjacent waves?

``````a. trough

-->  b. wavelength

c. amplitude

d. crest
``````

How is the length of a wave calculated?

``````-->  a. By measuring the distance between two corresponding points on adjacent waves.

b. by measuring the distance between the crest and the resting position

c. By measuring the direction of wave motion

d. By measuring the distance between the crest and the through
``````

What are the maximum and minimum values called in a transverse wave?

``````a. Length and Amplitude

-->  b. Crest and Trough

c. Density and Trough

d. Crest and Length
``````

How many crests and trough make one complete cycle of wave signal?

``````-->  a. 1 crest and 1 trough

b. 1 crest and 2 troughs

c. 2 crests and 1 trough

d. 2 crest and 2trough
``````

How many waves can be seen on the top of the horizontal line?

``````a. 3

-->  b. 5

c. 7

d. 6
``````

It has lower density and in the negative direction of disturbance.

``````a. crest

b. wave

c. amplitude

-->  d. Trough
``````

What is the measurement from the equilibrium position of particles or magnetic fields to the crest called?

``````a. frequency

-->  b. amplitude

c. wave length

d. trough
``````

From the diagram, identify what does (D) represent.

``````a. trough

b. crest

-->  c. wavelength

d. amplitude
``````

What is the distance between A and b?

``````-->  a. wavelength

b. A + D

c. C

d. D
``````

In the diagram, how many upward curves are there?

``````a. 3

b. 0

-->  c. 2

d. 1
``````

From which points do you measure a wavelength?

``````a. A to E

-->  b. B to F

c. D to H

d. C to G
``````

From the diagram, how many full wavelengths are there?

``````a. 1

b. 4

-->  c. 2

d. 3
``````

How many peaks are there in the wave?

``````a. 4

b. 3

c. 5

-->  d. 2
``````

What does point D to point H measure?

``````-->  a. Wavelength

b. Crest

c. Amplitude

d. Trough
``````

What kind of wave is depicted in the diagram shown below?

``````-->  a. transverse wave

b. longitudinal  wave

c. wavelength

d. amplitude
``````

It is One half the full extent of a vibration, oscillation, or wave

``````a. wavelength

b. chart

-->  c. Amplitude

d. time
``````

From the diagram, how many full wavelengths are there?

``````-->  a. 2

b. 4

c. 1

d. 3
``````

How many wave crests are present in the diagram?

``````a. 3

-->  b. 2

c. 1

d. 4
``````

Does the amplitude of a wave affect its wavelength?

``````a. Sometimes

b. Intermittently

c. No

-->  d. Yes
``````

What happens when amplitude increases?

``````-->  a. Nothing happens

b. Wavelength remains same

c. Wavelength decreases

d. Wavelength increases
``````

What is the measurement from the resting position of particles or magnetic fields to the wave crest called?

``````a. wave crest

-->  b. amplitude

c. wavelength

d. wave height
``````

What Greek letter represents wavelength?

``````-->  a. Lambda

b. Beta

c. Gamma

d. Alpha
``````

According to the diagram, how is this curve's wavelength measured?

``````-->  a. From one wave crest to the next one

b. The amplitude

c. From wave trough to the next wave trough

d. The wave height
``````

Where is a wave trough located?

``````a. Above the wave crest.

b. At the bottom of the amplitude.

-->  c. At the bottom of the wave height.

d. At the top of the wave height.
``````

How many parts of an analog signal is shown in the diagram?

``````a. 6

b. 3

-->  c. 5

d. 4
``````

How many wave crests are shown in the diagram?

``````-->  a. 4

b. 3

c. 2

d. 1
``````

What would happen if there is a decrease in wavelength?

``````a. wave frequency is constant

-->  b. wave frequency increases

c. wave frequency is halved

d. wave frequency decreases
``````

This is the height of the wave.

``````-->  a. Amplitude

b. Wavelength

c. Crest

d. Phase
``````

How many arrows can you see in the illustration?

``````-->  a. 5

b. 3

c. 4

d. 6
``````

What is the measurement from the wave trough to wave crest called?

``````-->  a. amplitude

b. wavelength

c. oscillation

d. frequency
``````

Which number corresponds to amplitude?

``````a. 4

b. 3

c. 2

-->  d. 1
``````

Which arrow shows the wave both at its highest and its lowest?

``````a. 1

b. 3

-->  c. 2

d. 4
``````

How many wave cycles are shown in this diagram?

``````a. 4

b. 3

c. 2

-->  d. 1
``````

Which number corresponds to the amplitude of this wave?

``````a. 2

b. 3

c. 4

-->  d. 1
``````

This is called the amplitude of the wave.

``````a. 4

b. 3

-->  c. 1

d. 2
``````

Wavelength is the distance between two corresponding points on adjacent waves: Crest and Trough. Crest is having the amplitude in positive direction while the Trough has the amplitude with negative direction. From the explanation, what is number 4?

``````a. crest

b. amplitude

-->  c. wavelength

d. trough
``````

From the diagram, what point comes after reaching crest?

``````a. elevation

b. amplitude

c. wavelength

-->  d. trough
``````

From the diagram, how many troughs are there?

``````a. 1

b. 2

-->  c. 3

d. 4
``````

How many trough points are shown in the diagram?

``````a. 2

b. 4

-->  c. 3

d. 1
``````

What is the maximum distance the particles of a medium move from their resting position when a wave passes through?

``````a. Crest

-->  b. Amplitude

c. Trough

d. Elevation
``````

What is the measurement from the resting position of particles or magnetic fields to the wave crest called?

``````a. elevation

-->  b. amplitude

c. wavelength

d. trough
``````

In the diagram, which color represents the wave with the shortest wavelength?

``````-->  a. Green

b. Blue

c. Red

d. All three waves have equal wavelengths.
``````

What is the Trough?

``````a. -1 cm

-->  b. -2 cm

c. 1 cm

d. 0 cm
``````

What is the variance on each side of the graph?

``````a. 6

-->  b. 2

c. 8

d. 1
``````

How many crests are found in the diagram of waves?

``````-->  a. 4

b. 1

c. 2

d. 3
``````

What is the name of the highest part of the wave?

``````a. Amplitude

b. Equilibrium

-->  c. Crest

d. Trough
``````

What is the lowest part of the transverse wave called?

``````a. crest

-->  b. trough

c. amplitude

d. equilibrium
``````

From the diagram, after reaching the highest point 'crest', what point does it reach next?

``````a. wave

-->  b. trough

c. amplitude

d. wavelength
``````

How many crests are in the diagram below?

``````a. 2

b. 4

-->  c. 3

d. 6
``````

How do you find the amplitude of a wave?

``````a. It is the length of the wave.

b. It is the length multiplied by the width of the wave.

-->  c. It is the height of the wave.

d. It is the width of the wave.
``````

What do you call the time required for two successive wave crests to pass a fixed point?

``````a. Wave Amplitude

b. Wavelength

c. Wave Frequency

-->  d. Wave Period
``````

What is the measurement between two sequential crests called?

``````a. amplitude

b. oscillation

-->  c. period

d. frequency
``````

Identify the Amplitude

``````a. X

-->  b. S

c. Y

d. X
``````

Identify the crest

``````-->  a. V

b. E

c. L

d. T
``````

Identify phase

``````a. 0

-->  b. T

c. U

d. Y
``````