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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

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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?

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


Question?

Why does the pulse flip over (invert)?


Question?

What does it take to make a downward wave?

a force


Question?

What exerts this force?

Spring pulls hand up

therefore

hand pulls spring down.


Question?

Which pull is bigger?

Neither – both the same (3rd law)

Students think person is bigger, thus pulls harder


Question?

Why does spring change directions and not the holder?

Spring has less inertia


Investigate

Make a standing wave


Question?

What is it?

“A traveling wave?”

But I don’t see it traveling.

I see up and down motion.


Question?

How long before the pulse repeats itself?


Investigate

Make an upward pulse.


Question?

What does the pulse do?

Bounces back as a downward pulse.

Reflects from me as an upward pulse.


Question?

How often does it repeat itself?

Repetitive distance is 2L

Will call this distance a wavelength.


Investigate

Send a little pulse on top of a standing wave.


Question?

How long does it take to return?

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


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.


Question?

What happened to the velocity of the pulse?

Varies depending on the length.


Question?

How can one make the wavelength smaller?

Use less of the spring.


Investigate

Create a pulse using half the spring.

What do you observe?

The pulse takes less time to go down and back.


Question?

What does shortening the length of spring change?

It decreases the wavelength.

with an increases in the

frequency (f)


Investigate

Shake slinky faster.

Results?

More reputations per minute

Greater Frequency


Investigate

Pull some of the spring into your hand.

Send some pulses.


Question?

What changes take place?

Made it tighter.

Results?

Tighter - Greater Restoring Force

Less Inertia - Easier to Move


Question?

How many humps can we make?


Investigate

Shake spring until there are 2 humps.

What is at either end? Middle?

Region of no movement - node

What is between?

Antinode


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.


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.)


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


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

v = f x

‘v’ is velocity

‘f’ is frequency

‘’ is wavelength


Investigate

Attach string to one end of the spring.

Make a pulse

What happens to pulse?

Reflects on same side at string end.


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.


Conclusion

It must travel 4L before it repeats itself


Question?

Why does pulse come back on the same side?

String has much less inertia.

What is at the string end?

An antinode.


Question?

What is at the other end of the spring?

Node

How long is the spring in ’s?

1/4 


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


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


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


Conclusion

A string instrument has a node at both ends.

Thus the overtones are hole multiple of the fundamental frequency.


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


Question?

What is a trumpet?

What is a violin?


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