Quick organ pipe/tube problem

What is the resonant frequency of a tube that is 0.4-m long?  Assume that the speed of sound is 340 m/s.

What are the frequencies of the next 2 harmonics in this tube?

Doppler effect

Doppler effect!

http://www.lon-capa.org/~mmp/applist/doppler/d.htm

The key in the Doppler effect is that motion makes the "detected" or "measured" frequencies higher or lower.

If the source is moving toward you, you detect/measure a higher frequency - this is called a BLUE SHIFT.

If the source is moving away from you, you detect/measure a lower frequency - this is called a RED SHIFT. Distant galaxies in the universe are moving away from us, as determined by their red shifts. This indicates that the universe is indeed expanding (first shown by E. Hubble). The 2011 Nobel Prize in Physics went to local physicist Adam Riess (and 2 others) for the discovery of the accelerating expansion of the universe. Awesome stuff!

http://www.nobelprize.org/nobel_prizes/physics/laureates/2011/

It's worth noting that the effect also works in reverse. If you (the detector) move toward a sound-emitter, you'll detect a higher frequency. If you move away from a detector move away from a sound-emitter, you'll detect a lower frequency.

Mind you, these Doppler effects only happen WHILE there is relative motion between source and detector (you).

And they also work for light. In fact, the terms red shift and blue shift refer mainly to light (or other electromagnetic) phenomena.

Sites from class today AND HW (for next Tuesday)

Some of these are repeats from the other day:

Anna-Maria

https://www.youtube.com/watch?v=vC9Qh709gas

https://www.youtube.com/watch?v=UHTF1-IhuC0&feature=iv&src_vid=vC9Qh709gas&annotation_id=annotation_1970696487

https://www.youtube.com/watch?v=WlDi2XpK_dQ


Shattering wineglass

https://www.youtube.com/watch?v=cPALfz-6pnQ


Ruben's tube (from me)

https://www.youtube.com/watch?v=cqilJNsiqig


Longitudinal vs. transverse waves

http://www.animatedscience.co.uk/blog/wp-content/uploads/focus_waves/tl-wave.html

Animated:

http://www.acs.psu.edu/drussell/Demos/waves/wavemotion.html

http://www.acs.psu.edu/drussell/Demos/rad2/mdq.html


Wave forms in tubes

http://www.acs.psu.edu/drussell/Demos/StandingWaves/StandingWaves.html


>

Practice problems:

Consider the musical note G, 392 Hz.  Find the following:

1.  The frequencies of the next two G's, one and two octaves above.

2.  The frequency of the G one octave lower than 392 Hz.

3.  The frequency of G#, one semi-tone (piano key or guitar fret) above this G.

4.  The frequency of A#, 3 semi-tones above G.

5.  The wavelength of the 392 Hz sound wave, assuming that the speed of sound is 340 m/s.

6.  What are the differences between longitudinal and transverse waves?  Gives examples of each.  What type of wave is sound?

7.  Use graphsketch.com/ and try to graph some functions.  Set the x-range as -6.3 to +6.3, and the y-range from -4 to +4.  Then graph these:

y = 3 sin(x)
y = sin(2x)
y = sin(x) + cos(x)
y = 2 sin(x) - 3cos(x)

Play around with anything that looks fun.  No need to write anything or print anything out - just play around with graphsketch.  If you're feeling ambitious, have a look at desmos.com.

PS.  I chose the x-range as I did because graphsketch uses radians (not degrees).  6.3 is close to 2pi, and 2pi is equal to 360 degrees.

Plan on a test next Thursday.  Yay!

HW due Friday (10/23)

Part 1

Review the concepts of how we make musical scales, in light of the equal-tempered scale.  Worth a look, if you have time:

https://en.wikipedia.org/wiki/Equal_temperament

Of particular note (heh, get it?):

Twelve tone equal temperament took hold for a variety of reasons. It conveniently fit the existing keyboard design, and permitted total harmonic freedom at the expense of just a little impurity in every interval. This allowed greater expression through enharmonic modulation, which became extremely important in the 18th century in music of such composers as Francesco Geminiani, Wilhelm Friedemann Bach, Carl Philipp Emmanuel Bach andJohann Gottfried Müthel.

With what we learned in class in mind, find the frequencies of:

A (one octave above concert A)
A (two octaves above concert A)
A (one octave below concert A)
A# (one semi-tone above concert A)
B (two semi-tones above concert A)

Recall that concert A is 440 Hz, and our multiplier (the 12th root of 2) is 1.059.

Part 2

Come to class with definitions of longitudinal and transverse waves.  Also, review these pages;


http://www.acs.psu.edu/drussell/Demos/waves/wavemotion.html

http://www.animatedscience.co.uk/blog/wp-content/uploads/focus_waves/tl-wave.html

http://www.acs.psu.edu/drussell/Demos/rad2/mdq.html


FYI, the device I used in class today was called a Ruben's tube.

Wave-age.

Wave practice!

Work out in your notes.  These will be reviewed on Friday.

Recall also:

v = f l

c = 3 x 10⁸ m/s (speed of light, including any type of electromagnetic wave)

1.  What is the wavelength of the radio station 97.9 ("98 Rock").  Keep in mind that the number refers to the frequency in MHz, and note that MHz means 'million (x 10⁶) Hz."

2.  The visible range of human eyesight is 700 nm to 400 nm.  What are the frequencies associated with this, and which end is red and which is violet?

3.  Find the speed of a 500 Hz wave with a wavelength of 0.4 m.

4.  What is the frequency of a wave that travels at 24 m/s, if 3 full waves fit in a 12-m space?  (Hint:  find the wavelength first.)

5.  Approximately how much greater is the speed of light than the speed of sound?

6.  Harmonics

a.  Draw the first 3 harmonics for a wave on a string.

b.  If the length of the string is 0.5-m, find the wavelengths of these harmonics.

c.  If the frequency of the first harmonic (n = 1) is 15 Hz, find the frequencies of the next 2 harmonics.

d.  Find the speeds of the 3 harmonics.  

7.  (Review) Differentiate between mechanical and electromagnetic waves.  Give examples.

9.  (Review) Draw a wave and identify the primary parts (wavelength, crest, trough, amplitude).

10.  The note C vibrates at 262 Hz (approximately).  Find the frequencies of the next two C’s (1 and 2 octaves above this), and the frequency of the C below it.

11.  A red LED has a wavelength of 662 nm.  What is the frequency of light emitted from it?  (nm refers to x 10^-9 m)

Also...

DRAFT for this lab is due Thursday, 10/15.  Final lab will be due the class after that (Monday).

Ok?  OK!

Lab handout FYI

Harmonics on a string

A special area of wave physics involves "harmonics on a string."  Harmonics arise due to reflected waves interfering with incoming waves.  At the right frequencies, resonance occurs - so, the "standing wave" can get a pretty big amplitude with minimal energy input.  This phenomenon is a lot like pumping the swings to make yourself go higher.  In general, a string has a lowest possible frequency (the "resonant frequency") at which it will vibrate naturally - imagine plucking a string and hearing the note that results.  However, there are other frequencies ("harmonics") that can be produced that will also cause familiar wave patterns.  That's what today's lab is all about.

In this lab, you will determine the relationships relevant for harmonics on a string.  First, some definitions:

harmonic number, n

- this is the number of "humps" or "half-waves" present on a string.  The sequence starts at 1 and goes up higher and higher (by integers) until the string doesn't exhibit much wave motion to the naked eye (though indeed there may still be harmonics)

wavelength, lambda (l)

- literally, the size of a complete wave.  Crest-to-crest or trough-to-trough distance.  Could also be the distance between any 2 points in phase with each other

frequency, f

- the number of waves or vibrations or oscillations per second

wave speed, v

- the rate at which the wave energy travels.  Could conceivably be measured with a stopwatch, but is better computed with the equation:  v = f l

Procedure

Set up a wave oscillator apparatus, with a pulley attached to a table.  Your string will be draped over the pulley.  Make sure the string is firmly attached to the oscillator and a weight is attached to the end of the string.

Measure the effective length of the string:  from oscillator to top of pulley.  Also measure the hanging mass.

Part I

1.  Starting very low, find the lowest possible frequency (on the sine wave generator) that gives you an n=1 (lowest) harmonic -- this is ONE hump.  Record frequency.

2.  Gradually increase the frequency, advancing through a series of harmonics.  Record n and f.  Do as many harmonics as you can. 

3.  In a table, record n, f, l and v.  You will need to calculate l and v.

Determine trends worth noting.

Part II

Chat with other groups – those who used a different hanging mass.  See if you can determine if there are differences due to the weight that hangs (and provides tension in the string).

Questions

1.  What seems to be clear from your data in part I?

2.  What seems to be clear from your data in part II?

3.  You may not play a stringed instrument, but what can you infer from your experiment as it relates to guitars, violins, etc.?

4.  Write a general conclusion – things you learned, things that were interesting, sources of error (threats to validity), suggestions for improving the experiment, and so forth.

Your complete lab report should include:  a title, date(s) performed, lab partner(s), purpose of lab (at the beginning), data, graphs (if relevant), pictures (if helpful), sample calculation (though all calculations will be done), conclusion and answers to questions.

Lab guidelines

Calculations:

Wavelength:  2L/n

Determine the speed of the wave for each trial, using the expression:  speed = frequency x wavelength.  The speed values should be in the data table.

The data table should have:  harmonic number (n), frequency, wavelength, speed.  Mass and length must be somewhere as well (or in the table).

In your conclusion, discuss the mathematical relationships you've found.  For example, how are frequency and harmonic number related?  How does tension affect the frequency?  For that question, you'll need to chat with other lab groups.

Also include sources of error for this experiment.

Basic structure of the lab report:

Title

Purpose of lab

Data table

Sample calculation for speed (your data table will have ALL of the calculated values, but there is only need for one calculation to be shown)

Graph(s), where relevant

Conclusion - probably the biggest, most detailed part of the lab.  This will have answers to lab questions (unless you wish to have a separate section for those), sources of error, ways to improve the experiment, anything interesting you learned, problems you faced in the lab, etc.

HW

Come to class with a definition of "standing waves" and "harmonics".