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Making career connections

Piano tuners use beats routinely in their work. When comparing a note with a tuning fork, they listen for beats and adjust the string until the beats go away (to zero frequency). For example, if the tuning fork has a 256 Hz size 12{"256"``"Hz"} {} frequency and two beats per second are heard, then the other frequency is either 254 size 12{"254"} {} or 258 Hz size 12{"258"`"Hz"} {} . Most keys hit multiple strings, and these strings are actually adjusted until they have nearly the same frequency and give a slow beat for richness. Twelve-string guitars and mandolins are also tuned using beats.

While beats may sometimes be annoying in audible sounds, we will find that beats have many applications. Observing beats is a very useful way to compare similar frequencies. There are applications of beats as apparently disparate as in ultrasonic imaging and radar speed traps.

Imagine you are holding one end of a jump rope, and your friend holds the other. If your friend holds her end still, you can move your end up and down, creating a transverse wave. If your friend then begins to move her end up and down, generating a wave in the opposite direction, what resultant wave forms would you expect to see in the jump rope?

The rope would alternate between having waves with amplitudes two times the original amplitude and reaching equilibrium with no amplitude at all. The wavelengths will result in both constructive and destructive interference

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Define nodes and antinodes.

Nodes are areas of wave interference where there is no motion. Antinodes are areas of wave interference where the motion is at its maximum point.

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You hook up a stereo system. When you test the system, you notice that in one corner of the room, the sounds seem dull. In another area, the sounds seem excessively loud. Describe how the sound moving about the room could result in these effects.

With multiple speakers putting out sounds into the room, and these sounds bouncing off walls, there is bound to be some wave interference. In the dull areas, the interference is probably mostly destructive. In the louder areas, the interference is probably mostly constructive.

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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

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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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

the definition of photon
Bright Reply
8kg of a hot liquid initial T is 90°© is missed with another liquid 3kg at 20° calculate e équilibrium T
Balki Reply
8kg of a hot liquid initial T is 90°© is missed with another liquid 3kg at 20° calculate e équilibrium T
answer plz
what are the products when acid and base mixed?
salt and water
What's this place about?
@Austin your answer should be SALT and WATER
salts and water
what work done
Dennis Reply
work done is the product of force and distance moved in the direction of force
Work done = force (F) * distance (D)
what is resounance
explain the three laws of isaac Newton with the reference
glory Reply
1st law ; a body will continue to stay at a state of rest or continue to move at a uniform motion on a straight line unless an external force is been acted upon
3rd law; in every action there is an equal or opposite reaction
2nd law: F=ma
why am i not having access to the Link in your exemples /figures ?
Augustine Reply
what is circut
hasiya Reply
newtons law of motion
First law:In an inertial frame of reference, an object either remains at rest or continues to move at a constant velocity, unless acted upon by a force.
is the ability to do work
Adjah Reply
u from
any body online hain
ability to do work is energy
what is energy
Mercy Reply
energy is ability of the capacity to doing work
what is vector
mosco Reply
A quantity that has both magnitude and direction
can a body with out mass float in space
Is the quantity that has both magnitude and direction
Yes it can float in space,e.g.polyethene has no mass that's why it can float in space
that's my suggestion,any other explanation can be given also,thanks
A charge of 1.6*10^-6C is placed in a uniform electric field in a density 2*5^10Nc^-1, what is the magnitude of the electric force exerted on the charge?
Omotosho Reply
what's phenomena
Enoch Reply
Phenomena is an observable fact or event.
Prove that 1/d+1/v=1/f
James Reply
What interference
Moyinoluwa Reply
What is a polarized light called?
what is a half life
Mama Reply
the time taken for a radioactive element to decay by half of its original mass
what is radioactive element
Half of the total time required by a radioactive nuclear atom to totally disintegrate
radioactive elements are those with unstable nuclei(ie have protons more than neutrons, or neutrons more than protons
in other words, the radioactive atom or elements have unequal number of protons to neutrons.
state the laws of refraction
state laws of reflection
Why does a bicycle rider bends towards the corner when is turning?
When do we say that the stone thrown vertically up wards accelerate negatively?
Give two importance of insulator placed between plates of a capacitor.
Macho had a shoe with a big sole moving in mudy Road, shanitah had a shoe with a small sole. Give reasons for those two cases.
when was the name taken from
Biola Reply
retardation of a car
when was the name retardation taken
did you mean a motion with velocity decreases uniformly by the time? then, the vector acceleration is opposite direction with vector velocity
what's velocity
Velocity is the rate of change of displacement
Practice Key Terms 8

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Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
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