Waves and periodic motion

Question 1

What is a wave?

Answer 1

A wave is a disturbance in a medium such that each particle in the medium vibrates about an equilibrium point in a simple harmonic (periodic) motion

Question 2

What is wavelength (λ)?

Answer 2

The distance from crest to crest (or valley to valley) of a transverse wave.

In a longitudinal wave, the wavelength is the distance from one rarefaction (or condensation) to another.

Question 3

What is amplitude (A)?

Answer 3

The maximum displacement of a particle in one direction from its equilibrium point.

Question 4

What is intensity (I)?

Answer 4

The square of the amplitude: A^2

Question 5

What is frequency? (f)

Answer 5

The number of cycles per unit time (per second)

Question 6

What is period (T)?

Answer 6

The duration of one cycle, it is the inverse of the frequency.

T = 1/f

Question 7

What is velocity (of a wave)? How is it calculated?

Answer 7

v of a wave is the velocity of the propagation of the disturbance that forms the wave through the medium.

The velocity is inversely proportional to the inertia of the medium. It can be calculated according to the following important equation:

v = λf

Question 8

What does the superposition principle state?

Answer 8

That the effect of two or more waves on the displacement of a particle is independent. The final displacement of the particle is the resultant effect of all the waves added algebraically, thus, the amplitude may increase or decrease.

Question 9

What is wave interference? What are the five criteria for this?

Synchrony sources
Coherent vibrations
Parallel vibrations
Interference conditions
Beat frequency

Answer 9

The summation of the displacements of different waves in a medium. There are 5 criteria

• Synchrony sources: vibration emitted by synchrony sources have the same phase
• Coherent vibrations: the phase of the vibrations are related, this means that the duration of the light impressions on the retina is much longer than the duration of a wave train between two emissions
• Parallel vibrations: the displacements of parallel vibrations keep parallel directions in space
• Interference conditions: two or more vibrations can interfere only when they are coherent, parallel and have the same period
• Beat frequency: The difference in frequency of two waves creates a new frequency

Question 10

What is constructive interference? Destructive interference?

Answer 10

Constructive interference: is when waves add to a larger resultant wave than either original

Destructive interference: is when the waves add to a smaller resultant wave than either original wave.

Question 11

What is resonance? (In wave//particle motion)

Answer 11

Forced vibrations occur due to a series of waves impinging upon an object. Natural frequencies are the intrinsic frequencies of a vibrating system.

If the forced vibration causes the object to vibrate at one of its natural frequencies, the body will vibrate at maximal amplitude, this is called resonance.

Since energy and power are proportional to the amplitude squared, they also are their maximum.

Question 12

What are standing waves? What are nodes?

Answer 12

Standing waves result when waves are reflected off a stationary object and back into the oncoming aves of the medium and superposition results.

Nodes are points where there is no particle displacement, which are similar to points of maximal destructive interference.

Question 13

What is the fundamental frequency?

Answer 13

• The lowest frequency in a harmonic (AKA first harmonic)

- The other are called overtones

Question 14

What are harmonic series?

Answer 14

Overtones whose frequencies are integral multiples of the fundamental (lowest) frequency (first harmonic)

Question 15

What are the three interference conditions?

Answer 15

Two or more vibrations can only occur if:

1. They are coherent (in phase)
2. Parallel
3. They have the same period

Question 16

The first harmonic has a frequency of 100 Hz. What is the period of the second harmonic?

Answer 16

The second harmonic has one extra node (and therefore an extra antinode), this effectively doubles the frequency of the second harmonic (eg. to 200 Hz)

Period is simply 1/f

So the answer is 1/200 = .005

(help with this division: think of what 200 must be multiplied to get 1000 (5), then think of what that must be divided by to get 1 (1000))

Question 17

If 2 is divided by 1000, how many decimal places are moved?

Answer 17

3, one for each zero :)

= .002

Question 18

If the first harmonic has a frequency of 100 Hz and a wavelength of 1 m, what is the frequency and wavelength of the second and third harmonic?

What is the speed of the waves?

Answer 18

First: 100 Hz, 1 m, 100 m/s

Second: 200 Hz, .5 m, 100 m/s

Third: 300 Hz, .33 m, 100 m/s

Speed is constant (as it is dependent on the medium, not the characteristics of the wave). Speed = (frequency)(wavelength)

Question 19

How can you figure out the period of a complex waveform?

Answer 19

You disregard all the little crests and troughs that make up the waveform, and instead look at all the repeating units. One repeating unit is one period.

Question 20

What is the speed of light?

Answer 20

3 x 10^8 m/s

Question 21

Give the relationship (formula) between wavelength, frequency and wave velocity

Answer 21

v = f⋅λ

This is useful when given the wavelength of something travelling at the speed of light (3 x 10^8 m/s)

Question 22

Mechanical waves in a medium, such as water, function to transport:

A. matter only
B. Energy only
C. Both matter and energy
D. Neither matter not energy

Answer 22

B. Energy only

Mechanical waves, such as sound and water waves, are a local oscillation of material. Only the energy propagates; the oscillating material does not move far from its initial equilibrium position.

Question 23

For a sound source that is moving away from an observer, why are the percentages of the change in frequency and wavelength much greater when sound waves are used instead of radio waves?

Answer 23

Sound waves travel more slowly.

The Doppler equation for frequency is Δf/f = -v/c for a given relative velocity v between source and detector. Thus, the frequency shift Δf depends inversely on the speed of the wave in the medium in which it propagates, c.

The velocity of sound is much smaller than that of electromagnetic radiation, so for the same relative velocity the frequency and wavelength shifts are much greater for sound than for radio waves.

Question 24

The fundamental, resonant wavelength of a pipe, open at both ends that is 1 m long and .1 m in diameter is ___ m?

Answer 24

2.0 m

Pipes and tubes have their resonant wavelengths when standing waves develop. An open pipe has its fundamental, resonant wavelength at twice the length of the pipe. Both ends have displacement antinodes (maximum amplitudes) with a node in the middle of the pipe. Thus, the pipe is half a wavelength long. The resonant wavelength is independent of the diameter of the pipe.

Question 25

How does the mass of an object on a pendulum effect the frequency of its oscillations?

Answer 25

It doesn’t!!

the formula for frequency (don’t need to memorize) is:

f = 1/2π√ (g/l)

Mass is not in the equation! Eg. a 100 kg mass on a 1 metre rope swings with the same frequency as a 1 kg mass.

Question 26

What happens when two pendulums are connected by a weak coupling (eg. spring)?

Answer 26

If they have similar frequencies, and if the energy starts in one oscillator, then the energy tends to be slowly transferred back and forth between the oscillators. This is called resonance.

When an opera singer sings in the same frequency as is natural for a wine glass, air carries enough energy to enter the glass and cause a nonlinear regime, and it bursts.

Question 27

What type of wave can be polarized, why?

Answer 27

Transverse waves can be polarized (confined to moving in one of two dimensions). Longitudinal waves cannot.

Transverse waves cause a disturbance in their medium that is perpendicular to the direction of the wave travel. Longitudinal waves are waves in which the displacement of the medium is in the same direction as, or the opposite direction to, the direction of travel of the wave. Mechanical longitudinal waves are also called compressional waves or compression waves, because they produce compression and rarefaction when traveling through a medium.

Question 28

Are water waves longitudinal, transverse or both?

Answer 28

Both

Question 29

Are waves on a plucked string longitudinal, transverse or both?

Answer 29

Transverse

Question 30

Are sound waves longitudinal, transverse or both?

Answer 30

Longitudinal (compression waves)

Question 31

Are earthquake waves longitudinal, transverse or both?

Answer 31

Both

Question 32

Are light waves longitudinal, transverse or both? What type of media do light waves travel through?

Answer 32

Transverse

These travel through a electric/magnetic field medium.

Question 33

A ball is thrown vertically upward from earth with velocity v, and returns to its original height in a time t. If the value of g were reduced to g/6 (as on the moon), how would t by changed?

Answer 33

t would increase by a factor of 6

The round trip time t for a ball thrown vertically is given by:

t = 2v/g

Question 34

When a ray of light enters a material that has a higher refractive index (eg. air to glass), will the refracted ray move towards or away from the normal?

With this in mind, is a critical angle more possible when going from air to glass, or from glass to air?

Answer 34

Towards.

This means that a critical angle is only really achievable when going from a higher refractive index (eg glass) to a lower one (eg. air).

Just remember, you won’t get total internal reflection by shining a light in glass, but you will when shining a light out of glass.

Question 35

What is the spring constant? What are its units?

Answer 35

A characteristic of a spring which is defined as the ratio of the force affecting the spring to the displacement caused by it.

k = N/m

AKA: k = newtons generated per metre length of spring

Question 36

A mass is connected to springs on either side of it. What is the spring constant in this case? Why?

Answer 36

The spring constant is 2k. This is because in order to move the mass, you must use twice as much force (F = -2kx).

Question 37

Most waves in the electromagnetic spectrum can be said to have a speed of what in a vacuum?

Answer 37

The speed of light

3 x 10^8

Question 38

A wave has a half-sine wave shape (L).

A lake has a propagation through it that causes a rise at one end, and a depression at the other. What is wavelength?

Answer 38

λ = 2L

Question 39

A pan of dry water is disturbed, causing sloshing. The sloshing oscillations persist for a long time. Why?

Answer 39

Energy conservation

It may be tempting to pick momentum conservation, but this is not the case, as velocity is not conserved, but amplitude.

Question 40

Why are very fast processes adiabatic?

Answer 40

They leave little time for energy transfer through media. Energy will instead usually be transformed into light.