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Phet explorations: wave interference

Make waves with a dripping faucet, audio speaker, or laser! Add a second source or a pair of slits to create an interference pattern.

Wave Interference

Test prep for ap courses

A guitar string has a number of frequencies at which it vibrates naturally. Which of the following is true in this context?

  1. The resonant frequencies of the string are integer multiples of fundamental frequencies.
  2. The resonant frequencies of the string are not integer multiples of fundamental frequencies.
  3. They have harmonic overtones.
  4. None of the above
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Explain the principle of superposition with figures that show the changes in the wave amplitude.

The student explains the principle of superposition and then shows two waves adding up to form a bigger wave when a crest adds with a crest and a trough with another trough. Also the student shows a wave getting cancelled out when a crest meets a trough and vice versa.

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In this figure which points represent the points of constructive interference?

Two wave generators are shown with their resulting rarefaction and compression marked. Points A, C, D, and E are at the intersection of two compression lines. Point B is at the intersection of two rarefaction lines. Point F is at the intersection of a compression line and a rarefaction line.
  1. A, B, F
  2. A, B, C, D, E, F
  3. A, C, D, E
  4. A, B, D
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A string is fixed on both sides. It is snapped from both ends at the same time by applying an equal force. What happens to the shape of the waves generated in the string? Also, will you observe an overlap of waves?

The student must note that the shape of the wave remains the same and there is first an overlap and then receding of the waves.

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In the preceding question, what would happen to the amplitude of the waves generated in this way? Also, consider another scenario where the string is snapped up from one end and down from the other end. What will happen in this situation?

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Two sine waves travel in the same direction in a medium. The amplitude of each wave is A , and the phase difference between the two is 180°. What is the resultant amplitude?

  1. 2 A
  2. 3 A
  3. 0
  4. 9 A

(c)

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Standing wave patterns consist of nodes and antinodes formed by repeated interference between two waves of the same frequency traveling in opposite directions. What are nodes and antinodes and how are they produced?

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Section summary

  • Superposition is the combination of two waves at the same location.
  • Constructive interference occurs when two identical waves are superimposed in phase.
  • Destructive interference occurs when two identical waves are superimposed exactly out of phase.
  • A standing wave is one in which two waves superimpose to produce a wave that varies in amplitude but does not propagate.
  • Nodes are points of no motion in standing waves.
  • An antinode is the location of maximum amplitude of a standing wave.
  • Waves on a string are resonant standing waves with a fundamental frequency and can occur at higher multiples of the fundamental, called overtones or harmonics.
  • Beats occur when waves of similar frequencies f 1 size 12{f rSub { size 8{1} } } {} and f 2 size 12{f rSub { size 8{2} } } {} are superimposed. The resulting amplitude oscillates with a beat frequency given by
    f B = f 1 f 2 . size 12{f rSub { size 8{B} } = lline f rSub { size 8{1} } - f rSub { size 8{2} } rline } {}

Conceptual questions

Speakers in stereo systems have two color-coded terminals to indicate how to hook up the wires. If the wires are reversed, the speaker moves in a direction opposite that of a properly connected speaker. Explain why it is important to have both speakers connected the same way.

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Problems&Exercises

A car has two horns, one emitting a frequency of 199 Hz and the other emitting a frequency of 203 Hz. What beat frequency do they produce?

f = 4 Hz size 12{f= {underline {"4 Hz"}} } {}

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The middle-C hammer of a piano hits two strings, producing beats of 1.50 Hz. One of the strings is tuned to 260.00 Hz. What frequencies could the other string have?

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Two tuning forks having frequencies of 460 and 464 Hz are struck simultaneously. What average frequency will you hear, and what will the beat frequency be?

462 Hz,

4 Hz

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Twin jet engines on an airplane are producing an average sound frequency of 4100 Hz with a beat frequency of 0.500 Hz. What are their individual frequencies?

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A wave traveling on a Slinky® that is stretched to 4 m takes 2.4 s to travel the length of the Slinky and back again. (a) What is the speed of the wave? (b) Using the same Slinky stretched to the same length, a standing wave is created which consists of three antinodes and four nodes. At what frequency must the Slinky be oscillating?

(a) 3.33 m/s

(b) 1.25 Hz

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Three adjacent keys on a piano (F, F-sharp, and G) are struck simultaneously, producing frequencies of 349, 370, and 392 Hz. What beat frequencies are produced by this discordant combination?

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Questions & Answers

Propose a force standard different from the example of a stretched spring discussed in the text. Your standard must be capable of producing the same force repeatedly.
Giovani Reply
What is meant by dielectric charge?
It's Reply
what happens to the size of charge if the dielectric is changed?
Brhanu Reply
omega= omega not +alpha t derivation
Provakar Reply
u have to derivate it respected to time ...and as w is the angular velocity uu will relace it with "thita × time""
Abrar
do to be peaceful with any body
Brhanu Reply
the angle subtended at the center of sphere of radius r in steradian is equal to 4 pi how?
Saeed Reply
if for diatonic gas Cv =5R/2 then gamma is equal to 7/5 how?
Saeed
define variable velocity
Ali Reply
displacement in easy way.
Mubashir Reply
binding energy per nucleon
Poonam Reply
why God created humanity
Manuel Reply
Because HE needs someone to dominate the earth (Gen. 1:26)
Olorunfemi
why god made humenity
Ali
Is the object in a conductor or an insulator? Justify your answer. whats the answer to this question? pls need help figure is given above
Jun Reply
ok we can say body is electrically neutral ...conductor this quality is given to most metalls who have free electron in orbital d ...but human doesn't have ...so we re made from insulator or dielectric material ... furthermore, the menirals in our body like k, Fe , cu , zn
Abrar
when we face electric shock these elements work as a conductor that's why we got this shock
Abrar
how do i calculate the pressure on the base of a deposit if the deposit is moving with a linear aceleration
ximena Reply
why electromagnetic induction is not used in room heater ?
Gopi Reply
room?
Abrar
What is position?
Amoah Reply
What is law of gravition
sushil Reply
Practice Key Terms 8

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Source:  OpenStax, College physics for ap® courses. OpenStax CNX. Nov 04, 2016 Download for free at https://legacy.cnx.org/content/col11844/1.14
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