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An Introduction To Waves. Created for CVCA Physics By Dick Heckathorn 16 May 2K+4. Apparatus. A long spring fastened to a support. What can one do with this spring? Can use this spring to communicate . Investigate. Quick up - down movement. What happens?

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An introduction to waves l.jpg

An Introduction To Waves

Created for CVCA Physics

By

Dick Heckathorn

16 May 2K+4


Apparatus l.jpg
Apparatus

A long spring fastened to a support.

What can one do with this spring?

Can use this spring to communicate.


Investigate l.jpg
Investigate

Quick up - down movement

What happens?

Up pulse goes to other end, flips over and returns upside down.


Question l.jpg
Question?

Why does the pulse flip over (invert)?


Question5 l.jpg
Question?

What does it take to make a downward wave?

a force


Question6 l.jpg
Question?

What exerts this force?

Spring pulls hand up

therefore

hand pulls spring down.


Question7 l.jpg
Question?

Which pull is bigger?

Neither – both the same (3rd law)

Students think person is bigger, thus pulls harder


Question8 l.jpg
Question?

Why does spring change directions and not the holder?

Spring has less inertia


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Investigate

Make a standing wave


Question10 l.jpg
Question?

What is it?

“A traveling wave?”

But I don’t see it traveling.

I see up and down motion.


Question11 l.jpg
Question?

How long before the pulse repeats itself?


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Investigate

Make an upward pulse.


Question13 l.jpg
Question?

What does the pulse do?

Bounces back as a downward pulse.

Reflects from me as an upward pulse.


Question14 l.jpg
Question?

How often does it repeat itself?

Repetitive distance is 2L

Will call this distance a wavelength.


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Investigate

Send a little pulse on top of a standing wave.


Question16 l.jpg
Question?

How long does it take to return?

The pulse returns in the same time it takes the hump to repeat itself.


Question17 l.jpg
Question?

What will happen to the time it takes a pulse to go down and back if the spring is shortened or lengthened?

Stays the same.


Question18 l.jpg
Question?

What happened to the velocity of the pulse?

Varies depending on the length.


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Question?

How can one make the wavelength smaller?

Use less of the spring.


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Investigate

Create a pulse using half the spring.

What do you observe?

The pulse takes less time to go down and back.


Question21 l.jpg
Question?

What does shortening the length of spring change?

It decreases the wavelength.

with an increases in the

frequency (f)


Investigate22 l.jpg
Investigate

Shake slinky faster.

Results?

More reputations per minute

Greater Frequency


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Investigate

Pull some of the spring into your hand.

Send some pulses.


Question24 l.jpg
Question?

What changes take place?

Made it tighter.

Results?

Tighter - Greater Restoring Force

Less Inertia - Easier to Move


Question25 l.jpg
Question?

How many humps can we make?


Investigate26 l.jpg
Investigate

Shake spring until there are 2 humps.

What is at either end? Middle?

Region of no movement - node

What is between?

Antinode


Investigate27 l.jpg
Investigate

Make 3, 4, 5 humps.

Get more humps by increasing f.

In fact, we are increasing the frequency in multiples of the fundamental which is the frequency that produced 1 hump.


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Conclusion

With a node at either end, one gets a sequence of natural frequencies that are multiples of the original (fundamental) frequency.

(Must have uniform tension.)


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Investigate

Make 2, 3, 4 and 5 humps

What happens to the number of half ’s?

The number changes by 1/2  from

1 to 2 to 3 to 4 to 5 half ’s


Conclusion30 l.jpg
Conclusion

If the number of half ’s increase from 1 to 2 to 3 to 4 to 5, then the wavelength must decrease from

2L/1 to 2L/2 to 2L/3 to 2L/4 to 2L/5

The frequency increases from

f to 2f to 3f to 4f to 5f


The wave equation l.jpg
The Wave Equation

v = f x

‘v’ is velocity

‘f’ is frequency

‘’ is wavelength


Investigate32 l.jpg
Investigate

Attach string to one end of the spring.

Make a pulse

What happens to pulse?

Reflects on same side at string end.


Question33 l.jpg
Question?

How far must it go to repeat itself?

Send ‘up’ pulse from held end.

At string end, come back as ‘up’ pulse.

At held end, goes back as ‘down’ pulse.

At string end, comes back as ‘down’ pulse.

At held end, goes back as ‘up’ pulse.


Conclusion34 l.jpg
Conclusion

It must travel 4L before it repeats itself


Question35 l.jpg
Question?

Why does pulse come back on the same side?

String has much less inertia.

What is at the string end?

An antinode.


Question36 l.jpg
Question?

What is at the other end of the spring?

Node

How long is the spring in ’s?

1/4 


Investigate37 l.jpg
Investigate

Make 2, 3, 4 and 5 humps

What happens to the number of quarter ’s?

The number changes by half  from

1 to 3 to 5 to 7 to 9 quarter ’s


Conclusion38 l.jpg
Conclusion

If the number of quarter ’s increase from 1 to 3 to 5 to 7 to 9, then the wavelength must decrease from

4L to 4L/3 to 4L/5 to 4L/7 to 4L/9

The frequency then increases by

f to 3f to 5f to 7f to 9f


Conclusion39 l.jpg
Conclusion

If a node is at both ends, the frequency changes by

f to 2f to 3f to 4f to 5f

If antinode is at one end and a node is at other, the frequency changes by

f to 3f to 5f to 7f to 9f


Conclusion40 l.jpg
Conclusion

A string instrument has a node at both ends.

Thus the overtones are hole multiple of the fundamental frequency.


Conclusion41 l.jpg
Conclusion

An instrument that has a node at one end and an antinode at the other

has overtones that are odd multiples of the fundamental frequency


Question42 l.jpg
Question?

What is a trumpet?

What is a violin?


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