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Math > Vibrations and Waves > Flashcards

Vibrations and Waves Flashcards

1
Q

Vibration

A

The repeated motion of a particle in a medium.

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2
Q

Cycle

A

One complete vibration (oscillation)

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3
Q

Wave

A

A disturbance that transfers energy over a distance

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4
Q

What are the 3 types of vibrations?

A

Transverse Vibration, Longitudinal Vibration, Torsional Vibration

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5
Q

Transverse Vibration

A

Object vibrates perpendicular to its axis. Ex: kid on swing, guitar string.

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6
Q

Longitudinal Vibration

A

Object vibrates parallel to the axis. Ex: baby jumper, shocks on car.

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7
Q

Torsional Vibration

A

Object twists back and forth around its axis.

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8
Q

Amplitude

A

Distance from equilibrium position to max displacement

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9
Q

Frequency

A

of cycles completed per unit time ( f = #cyc / total t )

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10
Q

Period

A

The time to complete one full cycle. ( T = total t / #cyc )

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11
Q

What is Periodic Motion?

A

Motion that occurs when the oscillation/vibration of an object repeats (exactly) in equal time intervals.

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12
Q

What is the universal wave equation?

A

V=fλ

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13
Q

What does a reflected pulse from a fixed end look like?

A

reflected and inverted

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14
Q

What does a reflected pulse from a free end look like?

A

reflected

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15
Q

What is the Principle of Superposition?

A

At any point on the medium the resulting amplitude is the algebraic sum of the two interfering amplitudes.

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16
Q

Define Wave

A

A periodic disturbance which transfers energy over a distance

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17
Q

What are the characteristics of a wave?

A

Crest: The region where the displacement is positive
Trough: The region where the displacement is negative
Amplitude (A): The distance above/below its equilibrium position to max displacement
Wavelength (λ): The distance between any consecutive points on the waves which are in phase (crest-crest)

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18
Q

Does amplitude of a pulse affect its speed?

A

No

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19
Q

Which is faster, the initial pulse or reflected pulse?

A

They should be equal.

20
Q

How do you make a wave go faster?

A

More force

21
Q

What happens to wavelength if frequency of vibrations is increased?

A

As frequency increases, wavelength decreases

22
Q

What is wave interference?

A

When two waves simultaneously act on the same particles in a given medium

23
Q

What are the two types of interference?

A

Destructive and Constructive interference

24
Q

Destructive Interference

A

The two amplitudes cause the waves to cancel out / reduce amplitude

25
Q

Constructive Interference

A

When two amplitudes build up creating a larger amplitude

26
Q

Node

A

Points at rest on a standing wave

27
Q

Anti node

A

Points between nodes which experience maximum displacement

28
Q

Why wont every frequency create a standing wave?

A

The λ and velocity must “fit” on the spring

29
Q

What happens when a wave moves to a slower medium?

A

If velocity decreases, λ decreases. The heavy/slow medium acts like a fixed end causing reflection to be inverted

30
Q

Resonant Frequency

A

The natural frequency at which an object vibrates best

31
Q

Mechanical Resonance

A

The transfer of energy from one object to another with the same natural frequency

32
Q

Sound Waves

A

A form of energy produced by a rapidly vibrating object. They are longitudinal vibrations which require a medium.

33
Q

Human Audible Range

A

20 Hz to 20 000 Hz

34
Q

Sound Intensity

A

Energy per unit area at a particular point per second measured in W/m^2

35
Q

Sound Intensity Level

A

Each increase by 10dB causes 10x as intense sound. Every 3dB increase doubles sound intensity.

36
Q

Hearing Loss/Protection

A

85dB = 8h max exposure. As the intensity doubles (safe) exposure time is cut in half.

37
Q

Resonance in closed air columns

A

1st resonant length = 1/4λ, 2nd r.l. = 3/4λ, 3rd r.l. = 5/4λ

38
Q

Resonance in open air columns

A

1st resonant length = 1/2λ, 2nd = 1λ, 3rd = 3/2λ

39
Q

Doppler effect

A

Moving towards = shorter λ, (Vw/Vw-Vs), fd > fs

Moving away = longer λ, (Vw/Vw+Vs), fd

40
Q

What are: (Vw), (Vs), (fs), (fd)

A

Vw: speed of wave, Vs: speed of source, fs: frequency of source, fd: observed (Doppler) frequency

41
Q

The Sound Barrier

A

As object velocity gets close to speed of sound, the highly compressed sound waves in front pile up and make it hard to break through

42
Q

Super-Sonic Speed

A

At speeds faster than the speed of sound, sound waves form a cone, trailing off behind (plane). Because the waves line up along the edges of the cone, we hear a sharp “crack” or sonic boom

43
Q

Mach Speed

A

Mach # = speed of object / speed of sound

44
Q

Beats

A

Two nearly identical sounds are played simultaneously and will both act constructively and destructively, producing alternating loud and quiet sound waves (beats).

45
Q

Beat frequency

A

f(beat) = I f2-f1 I

Math (19 decks)

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