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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


Dick Heckathorn

16 May 2K+4

Apparatus l.jpg

A long spring fastened to a support.

What can one do with this spring?

Can use this spring to communicate.

Investigate l.jpg

Quick up - down movement

What happens?

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

Question l.jpg

Why does the pulse flip over (invert)?

Question5 l.jpg

What does it take to make a downward wave?

a force

Question6 l.jpg

What exerts this force?

Spring pulls hand up


hand pulls spring down.

Question7 l.jpg

Which pull is bigger?

Neither – both the same (3rd law)

Students think person is bigger, thus pulls harder

Question8 l.jpg

Why does spring change directions and not the holder?

Spring has less inertia

Investigate9 l.jpg

Make a standing wave

Question10 l.jpg

What is it?

“A traveling wave?”

But I don’t see it traveling.

I see up and down motion.

Question11 l.jpg

How long before the pulse repeats itself?

Investigate12 l.jpg

Make an upward pulse.

Question13 l.jpg

What does the pulse do?

Bounces back as a downward pulse.

Reflects from me as an upward pulse.

Question14 l.jpg

How often does it repeat itself?

Repetitive distance is 2L

Will call this distance a wavelength.

Investigate15 l.jpg

Send a little pulse on top of a standing wave.

Question16 l.jpg

How long does it take to return?

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

Question17 l.jpg

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

What happened to the velocity of the pulse?

Varies depending on the length.

Question19 l.jpg

How can one make the wavelength smaller?

Use less of the spring.

Investigate20 l.jpg

Create a pulse using half the spring.

What do you observe?

The pulse takes less time to go down and back.

Question21 l.jpg

What does shortening the length of spring change?

It decreases the wavelength.

with an increases in the

frequency (f)

Investigate22 l.jpg

Shake slinky faster.


More reputations per minute

Greater Frequency

Investigate23 l.jpg

Pull some of the spring into your hand.

Send some pulses.

Question24 l.jpg

What changes take place?

Made it tighter.


Tighter - Greater Restoring Force

Less Inertia - Easier to Move

Question25 l.jpg

How many humps can we make?

Investigate26 l.jpg

Shake spring until there are 2 humps.

What is at either end? Middle?

Region of no movement - node

What is between?


Investigate27 l.jpg

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 l.jpg

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.)

Investigate29 l.jpg

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

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

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

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

It must travel 4L before it repeats itself

Question35 l.jpg

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

What is at the other end of the spring?


How long is the spring in ’s?

1/4 

Investigate37 l.jpg

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

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

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

A string instrument has a node at both ends.

Thus the overtones are hole multiple of the fundamental frequency.

Conclusion41 l.jpg

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

What is a trumpet?

What is a violin?