An Introduction To Waves Created for CVCA Physics By Dick Heckathorn 16 May 2K+4

A long spring fastened to a support. What can one do with this spring? Apparatus A long spring fastened to a support. What can one do with this spring? Can use this spring to communicate.

Quick up - down movement Investigate Quick up - down movement What happens? Up pulse goes to other end, flips over and returns upside down.

Why does the pulse flip over (invert)? Question? Why does the pulse flip over (invert)?

What does it take to make a downward wave? 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.

Students think person is bigger, thus pulls harder Question? Which pull is bigger? Neither – both the same (3rd law) Students think person is bigger, thus pulls harder

Spring has less inertia Question? Why does spring change directions and not the holder? Spring has less inertia

Investigate Make a standing wave

But I don’t see it traveling. Question? What is it? “A traveling wave?” But I don’t see it traveling. I see up and down motion.

How long before the pulse repeats itself? Question? How long before the pulse repeats itself?

Investigate Make an upward pulse.

Bounces back as a downward pulse. Reflects from me as an upward pulse. Question? What does the pulse do? Bounces back as a downward pulse. Reflects from me as an upward pulse.

How often does it repeat itself? Question? How often does it repeat itself? Repetitive distance is 2L Will call this distance a wavelength.

Send a little pulse on top of a standing wave. Investigate Send a little pulse on top of a standing wave.

How long does it take to return? 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.

What happened to the velocity of the pulse? Question? What happened to the velocity of the pulse? Varies depending on the length.

How can one make the wavelength smaller? Question? How can one make the wavelength smaller? Use less of the spring.

Create a pulse using half the spring. Investigate Create a pulse using half the spring. What do you observe? The pulse takes less time to go down and back.

What does shortening the length of spring change? Question? What does shortening the length of spring change? It decreases the wavelength. with an increases in the frequency (f)

More reputations per minute Investigate Shake slinky faster. Results? More reputations per minute Greater Frequency

Pull some of the spring into your hand. Investigate Pull some of the spring into your hand. Send some pulses.

What changes take place? Question? What changes take place? Made it tighter. Results? Tighter - Greater Restoring Force Less Inertia - Easier to Move

How many humps can we make? Question? How many humps can we make?

Shake spring until there are 2 humps. 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.

(Must have uniform tension.) 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.)

What happens to the number of half ’s? 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

The frequency increases from 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

Attach string to one end of the spring. Investigate Attach string to one end of the spring. Make a pulse What happens to pulse? Reflects on same side at string end.

How far must it go to repeat itself? 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.

It must travel 4L before it repeats itself Conclusion It must travel 4L before it repeats itself

Why does pulse come back on the same side? Question? Why does pulse come back on the same side? String has much less inertia. What is at the string end? An antinode.

What is at the other end of the spring? How long is the spring in ’s? Question? What is at the other end of the spring? Node How long is the spring in ’s? 1/4 

What happens to the number of quarter ’s? 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

The frequency then increases by 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

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

A string instrument has a node at both ends. Conclusion A string instrument has a node at both ends. Thus the overtones are hole multiple of the fundamental frequency.

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