The Phenomenon of Frequency and WavesThe Phenomenon of

Frequency and Waves

Chris Caliguire, Terry Darcy and Mike Woitach

Chris Caliguire, Terry Darcy and Mike Woitach

ObjectivesObjectives To learn and understand the equation velocity=λf and λ=velocity/f and how it works

To learn the relationship between wave length and velocity

To learn the relationship between frequency and velocity

To learn how to make different harmonic waves with a slinky

Learn how to draw open-open, closed-closed, and open-closed harmonic waves and some real life examples

Learn how standing waves are made Learn wave vocabulary Learn what beat frequencies are and how to find one Lean what the Doppler effect is Learn some experiments to do about waves

To learn and understand the equation velocity=λf and λ=velocity/f and how it works

To learn the relationship between wave length and velocity

To learn the relationship between frequency and velocity

To learn how to make different harmonic waves with a slinky

Learn how to draw open-open, closed-closed, and open-closed harmonic waves and some real life examples

Learn how standing waves are made Learn wave vocabulary Learn what beat frequencies are and how to find one Lean what the Doppler effect is Learn some experiments to do about waves

ExperimentsExperiments

Experiment 1 Experiment 1

Materials:A slinkyA partner or twoA stopwatchA ruler

Materials:A slinkyA partner or twoA stopwatchA ruler

Objective- Learn how frequency, wave length, and velocity are related

Safety precautionsSafety precautions

Always watch the ends of the slinky. Due to their metallic makeup the ends can be sharp, and possibly hazardous to your health and possibly life threatening

Always wear protective eye gear for extra safety

DO NOT EAT THE SLINKY OR ANY OTHER MATERIALS

Always watch the ends of the slinky. Due to their metallic makeup the ends can be sharp, and possibly hazardous to your health and possibly life threatening

Always wear protective eye gear for extra safety

DO NOT EAT THE SLINKY OR ANY OTHER MATERIALS

How to doHow to do Create standing waves using the slinky and

count the number of waves in one minute use this information to calculate frequency, then measure the wave length and use these pieces of information to calculate the velocity using the equations λ=velocity/f and v=λf then try increasing the frequency, and see how the velocity is affected. Then repeat by changing the wave length and see the affect again. Record your results and be amazed.

Create standing waves using the slinky and count the number of waves in one minute use this information to calculate frequency, then measure the wave length and use these pieces of information to calculate the velocity using the equations λ=velocity/f and v=λf then try increasing the frequency, and see how the velocity is affected. Then repeat by changing the wave length and see the affect again. Record your results and be amazed.

Observations about the experiment

Observations about the experiment

Frequency is directly related to velocity

Wave length is directly related to velocity

Frequency is directly related to wave length

Frequency is directly related to velocity

Wave length is directly related to velocity

Frequency is directly related to wave length

Experiment 2Experiment 2

Materials:A guitar stringA cupWeightsA partnerA stopwatch

Materials:A guitar stringA cupWeightsA partnerA stopwatch

Objective-find out how tension affects pitch

Safety precautionsSafety precautions

Always watch the ends of the guitar string. Due to their metallic makeup the ends can be sharp, and possibly hazardous to your health and possibly life threatening

Always wear protective eye gear for extra safety

DO NOT EAT THE GUITAR STRING OR ANY OTHER MATERIALS

Always watch the ends of the guitar string. Due to their metallic makeup the ends can be sharp, and possibly hazardous to your health and possibly life threatening

Always wear protective eye gear for extra safety

DO NOT EAT THE GUITAR STRING OR ANY OTHER MATERIALS

How to doHow to do

Attach the string to a stationary object and attach the cup to the other end. Put weights in the cup to create tension on the string. Then measure the frequency and then repeat by adding more weight and recalculate the frequency. Repeat a few times to get several pieces of data and see how the pitch changes (pitch=frequency)

Attach the string to a stationary object and attach the cup to the other end. Put weights in the cup to create tension on the string. Then measure the frequency and then repeat by adding more weight and recalculate the frequency. Repeat a few times to get several pieces of data and see how the pitch changes (pitch=frequency)

Observations Observations

Pitch and tension is directly related

Using this we can understand how a guitar works- push on a fret closer to the string, create a higher pitch by increasing the tension

Pitch and tension is directly related

Using this we can understand how a guitar works- push on a fret closer to the string, create a higher pitch by increasing the tension

The equation wavelength= velocity/frequency comes from the relationship between the amount of times the wave moves back and the tension of the medium. The more tension, the more speed that comes form the wavelength becoming longer. Increasing the tension is the only way to increase the wavelength, because you can’t make the wavelength longer by increasing the frequency or the speed. So the wavelength has to be the result of the action, that is why it is the result of the equation.

The harmonic of a wave refers to the number of Antinodes on a standing wave. To increase the harmonic you must increase frequency. But there are different types of standing waves there areClosed Closed, Open Open, and Open Closed. Open Open and Open Closed and Closed Closed standing waves can be created bysound. But it is impossible to create an open open or open closed wave on something such as a slinky

A=Antinodes N=Nodes

Amplitude

Wavelength

Middle Line

An open-open standing wave is called anOpen-open standing wave because thereare no nodes on either side leaving both sides “open”.

In an open-open standing wave:as the harmonic increases the number ofwaves increases by ½ starting with ½ of aWave being the first harmonic to the left are diagrams of open-open waves goingup to the 5th harmonic. An example of aWay to make an open-open wave is to blowInto a tube, creating an open-open sound wave.

In an open closed standing Wave for each harmonic there is anextra half of a wave, starting with the first harmonic being ¼ of a wave.At the left is a picture of Open-Closedwaves going up to the 5th harmonic. Away you could make an open closed wave Is by blowing into a test tube.

Open Closed waves are called open-Closedwaves because one side of the wave has anode, while the other side is does not, leaving it “open”

Closed Closed Standing waves arecalled that because they have nodeson each side, making the ends ofthe wave “closed”.

In a Closed-closed wave for each harmonic an additional half of a wave is added, starting with ½ ofa wave with nodes on each end. you can make closed-closed waveswith sound or vibrations or a slinky.on the left are diagrams of closed closed waves with increasing harmonics.

The UnitsThe UnitsΛ- The units for wavelength are Meters

Frequency- The Units for frequency are pulses over time orHertz.

Velocity- the units for velocity are Meters per Second

Types of WavesTypes of Waves

Pulse- One single waveLongitudinal-waves that go

forward and back with no amplitude.

Transverse-Waves that have an altitude but move forward and backward(not standing)

Pulse- One single waveLongitudinal-waves that go

forward and back with no amplitude.

Transverse-Waves that have an altitude but move forward and backward(not standing)

How to Measure WavesHow to Measure Waves

Amplitude- The height of the wave from the middle line.

Crest- Top arc of the waveTrough- Bottom arc of the

waveFrequency- Pulses/TimePeriod- Time/Pulses

Amplitude- The height of the wave from the middle line.

Crest- Top arc of the waveTrough- Bottom arc of the

waveFrequency- Pulses/TimePeriod- Time/Pulses

InterferenceInterference

Constructive interference- When something or another wave interferes with a wave, making it larger in amplitude.

Destructive interference- When something or a wave interferes with a wave, making it smaller in amplitude.

Constructive interference- When something or another wave interferes with a wave, making it larger in amplitude.

Destructive interference- When something or a wave interferes with a wave, making it smaller in amplitude.

Beat FrequenciesBeat Frequencies

Beat frequencies are the absolute value of the differences of two different sound waves. That’s about as simply as I can put it.

Beat frequencies are the absolute value of the differences of two different sound waves. That’s about as simply as I can put it.

The Doppler EffectThe Doppler Effect

As an object creates a sound and the sound waves start getting further and further away, the sound waves space out further away from one another. Also if an object making a sound is accelerating the sound waves bunch up in one area and in other areas they are extremely far away from eachother.

As an object creates a sound and the sound waves start getting further and further away, the sound waves space out further away from one another. Also if an object making a sound is accelerating the sound waves bunch up in one area and in other areas they are extremely far away from eachother.

QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.

The End (The section, it isn’t

actually the end)

The End (The section, it isn’t

actually the end)Terry, Mike, and ChrisTerry, Mike, and Chris

Summary Summary

In this chapter, you learned all about waves and how to understand how they move. We presented different equations based on the wavelength, frequency, and speed of the wave. Along with mathematical representations, we showed how to draw and interpret wave diagrams. We discussed different experiments you can do at home if you want to try and witness the physical phenomenon for yourself. We hope our chapter has increased your understanding of waves.

In this chapter, you learned all about waves and how to understand how they move. We presented different equations based on the wavelength, frequency, and speed of the wave. Along with mathematical representations, we showed how to draw and interpret wave diagrams. We discussed different experiments you can do at home if you want to try and witness the physical phenomenon for yourself. We hope our chapter has increased your understanding of waves.

Wave ProblemsWave Problems

11

What is the velocity of a wave with a frequency of 20Hz and a wavelength of 40 meters?

What is the velocity of a wave with a frequency of 20Hz and a wavelength of 40 meters?

1 1

40m times 20 Hz V= 80m/s

40m times 20 Hz V= 80m/s

22

A wave has a wavelength of 1m and a frequency of 20Hz, what is the velocity of the wave?

A wave has a wavelength of 1m and a frequency of 20Hz, what is the velocity of the wave?

22

1m times 20Hz V= 20m/s

1m times 20Hz V= 20m/s

33

What is the period of a wave that has a wavelength of 2m and a frequency of 3Hz?

What is the period of a wave that has a wavelength of 2m and a frequency of 3Hz?

33

Period is inversely proportional to the frequency; if the frequency is 3 than the period is 1/3 or 0.333.

Period is inversely proportional to the frequency; if the frequency is 3 than the period is 1/3 or 0.333.

44

If the speed of a wave is 3m/s, and the frequency is 1Hz, than what is the wavelength?

If the speed of a wave is 3m/s, and the frequency is 1Hz, than what is the wavelength?

44

Since the speed of the wave is wavelength times the frequency, to find the wavelength, you divide the speed by the frequency.

3/1= 3m

Since the speed of the wave is wavelength times the frequency, to find the wavelength, you divide the speed by the frequency.

3/1= 3m

55

If the wavelength of a wave is 5m and the period of the wave is 0.05, what is the speed of the wave?

If the wavelength of a wave is 5m and the period of the wave is 0.05, what is the speed of the wave?

55

Multiply the wavelength by the inverse of the period. Since the period is equal to 1/20, the frequency must be 20/1. So V=5(20)= 100m/s.

Multiply the wavelength by the inverse of the period. Since the period is equal to 1/20, the frequency must be 20/1. So V=5(20)= 100m/s.

66

If Tom Green observes that a wave with a wavelength of 5m moves back and forth 50 times in 10 seconds. How fast was the wave moving?

If Tom Green observes that a wave with a wavelength of 5m moves back and forth 50 times in 10 seconds. How fast was the wave moving?

66

The frequency is the number of waves per second, so if 50 waves occur in 10 seconds, the frequency is 5Hz.

V=5*5= 25m/s

The frequency is the number of waves per second, so if 50 waves occur in 10 seconds, the frequency is 5Hz.

V=5*5= 25m/s

77

On the ocean, a wave is 300cm long and has a speed of 12m/s. What is the frequency of the wave?

On the ocean, a wave is 300cm long and has a speed of 12m/s. What is the frequency of the wave?

77

300cm is equal to 3m, and since you know that the speed of the wave is 12m/s, you can divide 12 by 3 so frequency= 4Hz.

300cm is equal to 3m, and since you know that the speed of the wave is 12m/s, you can divide 12 by 3 so frequency= 4Hz.

88

Two students move a slinky up and down creating a standing wave. They measure that the wavelength is 50cm. Then they calculate that the period of the wave is .333. What is the speed of the wave they are witnessing?

Two students move a slinky up and down creating a standing wave. They measure that the wavelength is 50cm. Then they calculate that the period of the wave is .333. What is the speed of the wave they are witnessing?

88

Since the period is .333, to find the frequency, you find the inverse of period. In this case it is 3Hz. And you know the wavelength is 50cm, which becomes .5m. So, V=.5*3= 1.5m/s

Since the period is .333, to find the frequency, you find the inverse of period. In this case it is 3Hz. And you know the wavelength is 50cm, which becomes .5m. So, V=.5*3= 1.5m/s

99

Jack Nicholson is walking down the street when he witnesses two students making a standing wave on a slinky. He takes out his meter stick and measures that the wave has a wavelength of 1m. Then he counts that the wave moves back and forth 20 times in 10 seconds. What is the velocity of the wave that Jack is witnessing?

Jack Nicholson is walking down the street when he witnesses two students making a standing wave on a slinky. He takes out his meter stick and measures that the wave has a wavelength of 1m. Then he counts that the wave moves back and forth 20 times in 10 seconds. What is the velocity of the wave that Jack is witnessing?

99

The wavelength is 1m, and the frequency is number of waves divided by time. So the frequency is 2Hz. V= 2*1= 2m/s. The wave Jack saw was moving at 2m/s.

The wavelength is 1m, and the frequency is number of waves divided by time. So the frequency is 2Hz. V= 2*1= 2m/s. The wave Jack saw was moving at 2m/s.

1010

Ana the caterpillar queen blows across the top of a test tube creating a open-closed first harmonic wave. The height of the test tube is 25cm, and the speed of sound is 340m/s, what is the frequency of the wave?

Ana the caterpillar queen blows across the top of a test tube creating a open-closed first harmonic wave. The height of the test tube is 25cm, and the speed of sound is 340m/s, what is the frequency of the wave?

1010

Since a wave in the first harmonic is only ¼ of a wave, then you have to multiply the height by 4. So 25cm times 4 is 100cm, or 1m. To find the frequency you have to divide the speed of sound (340m/s) by 1m. So the frequency you come out with is 340Hz.

Since a wave in the first harmonic is only ¼ of a wave, then you have to multiply the height by 4. So 25cm times 4 is 100cm, or 1m. To find the frequency you have to divide the speed of sound (340m/s) by 1m. So the frequency you come out with is 340Hz.

1111

Tom Green is skateboarding down the street when he sees Glen Humplick making a wave on a string. The wave has a length of 60cm and it is moving with a frequency of 2Hz. What is the speed of Glen’s wave?

Tom Green is skateboarding down the street when he sees Glen Humplick making a wave on a string. The wave has a length of 60cm and it is moving with a frequency of 2Hz. What is the speed of Glen’s wave?

1111

Wavelength times frequency equals velocity, so V= .6*2= 1.2m/s.

Wavelength times frequency equals velocity, so V= .6*2= 1.2m/s.

1212

If a wave has a velocity of 5m/s and a frequency of 5Hz, then what is the wavelength of the wave?

If a wave has a velocity of 5m/s and a frequency of 5Hz, then what is the wavelength of the wave?

1212

Wavelength= velocity/ frequency, W= 5/5= 1m.

Wavelength= velocity/ frequency, W= 5/5= 1m.

1313

If the same wave from the previous problem’s speed increases to 10m/s, and the wavelength stays the same, what is the new frequency?

If the same wave from the previous problem’s speed increases to 10m/s, and the wavelength stays the same, what is the new frequency?

1313

F= w/ v, so F= 10/ 1= 10Hz.F= w/ v, so F= 10/ 1= 10Hz.

1414

If a sound wave in the second harmonic is created in a 10m tunnel that was closed on one end, and the speed of sound in air is 340m/s, what is the frequency of the wave?

If a sound wave in the second harmonic is created in a 10m tunnel that was closed on one end, and the speed of sound in air is 340m/s, what is the frequency of the wave?

1414

Second harmonic is only half a wave so the total wave length is 20m. F= v/ w, so F= 340/ 20= 17Hz.

Second harmonic is only half a wave so the total wave length is 20m. F= v/ w, so F= 340/ 20= 17Hz.

1515

What is the wavelength of a 1st harmonic wave made in a 15cm open-closed test tube?

What is the wavelength of a 1st harmonic wave made in a 15cm open-closed test tube?

1515

A 1st harmonic wave is ¼ of a wave, so you multiply .15m by 4. So you end up with 1m as the wavelength.

A 1st harmonic wave is ¼ of a wave, so you multiply .15m by 4. So you end up with 1m as the wavelength.