1. 5.1.4 Interference, Standing Waves, and Resonance
Guitar Strings and Crumbling Bridges

2. 2 Types of Interference:
U.G. Describe the Phenomena of Superposition & Wave Interference
Why the funky pattern?
Click sim.
2 Types of Interference:
Constructive: waves add up to become stronger
Destructive: waves add up to become weaker
Superposition causes INTERFERENCE

3. Introduction and Terms
INTERFERENCE – the result of two waves meeting in a medium.
CONSTRUCTIVE – results in greater amplitude.
DESTRUCTIVE – results in lower amplitude.
“In phase” interferes CONSTRUCTIVELY
“180° out of phase” interferes DESTRUCTIVELY

4. Example What is the direction of motion in the medium?
Both waves reach maximum
amplitude at that point!

5. Interference of Two Point Sources of Waves
When viewed from above, a wave source makes circular patterns
Ripple Tank
Simulation
TWO TROUGHS
CONSTRUCTIVE
crest (wave front)
trough
CRESTS AND TROUGH
DESTRUCTIVE
TWO CRESTS
CONSTRUCTIVE

6. Thick lines = Crests
Thin lines = Troughs
Thus: Red dots = constructive interference (2 crests or 2 troughs)
And: Blue dots = destructive interference (Meeting of a crest & trough)

7. True of all Longitudinal Waves
U.G. Describe the features of a Sound Wave & Superposition & Wave Interference
Anatomy of a Sound Wave
Rarefaction
Compression
True of all Longitudinal Waves
Low Prs
High Prs
Compression

8. Constructive Interference
U.G. Describe the features of a Sound Wave & Superposition & Wave Interference
Constructive Interference
Addition of In PHASE
wave points.
Results in a wave of
Larger amplitude
Need same f

9. Destructive Interference
U.G. Describe the features of a Sound Wave & Superposition & Wave Interference
Destructive Interference
Addition of Exactly
Out of PHASE wave points.
Results in a wave of
Zero amplitude
180 deg.

10. Total Destructive Interference Requirements
U.G. Describe the features of a Sound Wave & Superposition & Wave Interference
Total Destructive Interference Requirements
Must have 2 waves that are:
Traveling in Opposite Directions
Equal Amplitude & 180 degrees out of phase
Equal Frequency
Opposite Directions b/c 2 waves in the same medium in the same direction will never catch each other (same speed) to interfere

11. The Doppler Effect Predict the shape of the wave fronts
Predict the shape of the wave fronts
if the spider moves toward B

12. How's Frequency affected?
The Doppler Effect: Wave fronts of a moving source bunch up & spread out, causing a change in λ & f
for outside observer
How's Frequency affected?

14. Phenomenon #4 – Resonance
All mediums have a NATURAL FREQUENCY that corresponds to their atomic structure.
Exciting this frequency causes large AMPLITUDE vibrations in the medium
If the frequency is excited with enough ENERGY the medium may become damaged or even shatter.
If two materials have the same (or close) natural frequencies then vibrations may be passed from one material into the other.

15. So, how's that glassware thing work?
Resonance
All objects will oscillate (vibrate)
at their own natural frequency
Ex. Instruments, Dinner Glassware…..
A forced vibration
at the natural frequency causes
Try with slinky…
Ex. Push Child on a swing
Resonant frequency is the natural frequency of the glass… qhen you hit it that is the resonant frequency you hear…
Operah singers who break glass excite the glass at its natural resonance frequency raising its amplitude until the glass cant take it anymore and it breaks.
Bridge in 1940 blew bridge at the resonant frequency 2 hours before it broke
Energy Buildup
Amplitude Increase
causing
(Energy transferred at the natural frequency)
THis is Resonance
So, how's that glassware thing work?

16. Youtube Youtube2 Resonance In 1940, The Tacoma Narrows Bridge
Collapsed due to resonance
Click or
Mechanical Universe Video # 17: 2:50 & 21 min.
1831, Manchester England, Bridge collapsed due to soldiers marching in cadence
Bridge in 1940 blew bridge at the resonant frequency 2 hours before it broke
click
Youtube
Youtube2
Need Internet Connection

17. Phenomenon #3 – Standing Waves
When a wave encounters a fixed boundary it REFLECTS.
The reflected wave comes back through the original wave and they INTERFERE.
The result is a STANDING WAVE.
NODES : always 180° out of phase (destructive interference) - NO MOTION.
ANTINODES : alternate between in-phase and 180° out of phase –MAX MOTION.
Standing Waves

18. Standing Waves (String Harmonics)
UG: How’s a standing wave formed, and what features does it have?
Standing Waves (String Harmonics)
Waves traveling on a string will reflect and interfere, producing a standing wave, if they are at the resonant (natural) frequency.
Click
Fundamental Freq. for the stringwave.swf (Phet Sim) is around 8 Hz. Use 2 fixed ends. Then try it with a slinky in the hall.
NRG Xferred at the Natural f causing Energy buildup & Amp. Inc.
f1 = 8 Hz

19. Standing Waves (String Harmonics)
Waves traveling on a string will reflect and interfere, producing a standing wave, if they are at the resonant frequency.
CONDITION: 2 Waves of the same frequency (& amplitude), travel in opposite directions, super impose & interfere to produce Standing Waves
Don’t use multiple of fundamental f here: save for Strobe demo later. REINFORCE WITH SLINKY

20. Standing Waves (String Harmonics)
Incident & Reflected waves are IN PHASE to form Constructive Interference spots
Incident & Reflected waves are OUT OF PHASE to form Destructive Interference spots
UG: How’s a standing wave formed, and what features does it have?

21. Standing Waves: DRAW & LABEL
On a standing wave, wave “appears” to be fixed in space, changing in amplitude only
Antinode = spot of total
constructive interference (max. amplitude)
Black Line = Resultant Standing Wave
Node = spot of total
destructive interference (no amplitude)

22. Multiples of the Natural (Resonant) Frequency
String Harmonics:
Multiples of the Natural (Resonant) Frequency
Mech. Oscill. (SUNY)
Antinode = spot of total constructive interference (max. amplitude)
Node = spot of total destructive interference (no amplitude)

23. Practice
FOUR

24. Practice The grid below represents a 10 meter long string.
Sketch the standing wave that this string would produce if it were to have SIX nodes.
Draw a circle around each ANTINODE on the string.
Determine the wavelength of this standing wave. _________________m
Assuming that this wave moves at 2.0 meters per second, calculate its frequency and period. 4

25. String Harmonics Problems
The speed of waves in a particular guitar string is found to be 425 m/s. Determine the fundamental frequency (1st harmonic) of the string if its length is 76.5 cm.
Click to see solution
String Harmonics Problems
76.5 cm
UG: Discuss modes of vibration (2 fixed ends) & apply to solve problems

26. String Harmonics Problems
2) Determine the length of guitar string required to produce a fundamental frequency (1st harmonic) of 256 Hz. The speed of waves in a particular guitar string is known to be 405 m/s.
String Harmonics Problems
L = ???
UG: Discuss modes of vibration (2 fixed ends) & apply to solve problems