Waves - I

Question 1

Mechanical waves

Answer 1

Move through a medium

Ex: water waves, sound waves, seismic waves

Question 2

Electromagnetic waves

Answer 2

Light
Ex: x-rays, UV, IR
*don’t require a medium to propagate

Question 3

Matter Waves

Answer 3

Quantum mechanical description of nature

Describes physical world at short length scale, like molecules for example

Question 4

Transverse waves

Answer 4

The disturbance is perpendicular to the wave’s direction of travel

Slinky ex: your hand is moving up and down as the wave is traveling right wards

Ex: waves on string, water waves

Question 5

Longitudinal waves

Answer 5

The disturbance is PARALLEL to the direction of propagation

Slinky ex: your hand is moving left and right and so is the wave — you’re pushing onwards and out

Ex. Sound waves

Question 6

Traveling waves

Answer 6

Waves that move from one point to another (transverse and longitudinal)

Wave function y = y(x,t) = h(kx+ωt) plus or minus

Question 7

Sinusoidal Waves

Answer 7

Wave forms are described sine and cosine functions

y(x,t) = ym sin(kx- ωt)

Question 8

ym

Answer 8

Amplitude = Max displacement

Question 9

λ and κ

Answer 9

Wave length and Angular wave number:
Describes spatial dependence

k = 2π/λ

Question 10

T, f, ω

Answer 10

Period, frequency, angular frequency: describe TIME dependence

ω = 2πf/T

Question 11

φ

Answer 11

Phase constant: gives displacement at x = 0 and t = 0

Necesita para describir una ola genérica

y(x,t) = ym sin(kx+ ω + φ) *+/-

Question 12

Relationship between λ & κ

Answer 12

If POSITION changes by one wavelength, the the displacement should not change

Question 13

Relationship between T and ω

Answer 13

If TIME changes by one period, the the displacement should not change

ω=2π/T

Question 14

Speed of waves

Answer 14

Mesures how fast the pattern (shape) moves

Measured by following a point retaining its displacement

Question 15

Sinusoidal waves

Answer 15

A point retaining displacement has a constant phase

Question 16

Sinusoidal waves

Answer 16

A point retaining displacement has a constant phase.

y (x, t) = ym sin (kx − ωt) = (constant)
⟹ kx − ωt = (constant)
⟹ v =ω/k = λ/T = fλ

Question 17

y(x,t) = ym sin(kx+ ω) function is moving in the

Answer 17

negative direction

Question 18

Relationship between tension and wave speed

Answer 18

greater tension, the faster the wave travels

- the speed INCREASES as the tension, 𝜏 INCREASES

Question 19

Inertial property of a rope

Answer 19

the wave travels faster on a lighter rope

Question 20

Relationship between wave speed and linear mass density

Answer 20

the speed DECREASES as the linear density μ =M/L, INCREASES

Question 21

Wave speed on a stretched string

Answer 21

v = the square root of (τ/μ)

Question 22

Transverse speed (u)

Answer 22

measures how fast elements of a medium move in the oscillation direction
u = ∂y/∂t = − ωym cos (kx − ωt)

Question 23

Kinetic Energy

Answer 23

dK =1/2dmu^2 =1/2μdxω^2y^2mcos^2(kx − ωt)

Question 24

Transport of Kinetic Energy

Answer 24

(dK/dt)avg = 1/4 μvω^2y^2m

Question 25

An oscillating system

Answer 25

(KE) = (PE)

Question 26

Total Average Power

Answer 26

Pavg = 1/2μvω^2y^2m

Question 27

Principle of Superposition

Answer 27

Overlapping waves algebraically add to produce a net wave.

Overlapping waves do not alter motion of each other

Question 28

Standing Waves

Answer 28

If two waves with the same amplitude and frequency travel in opposite directions, their
interference produce a standing wave

Question 29

Exactly in phase wave

Answer 29

produces a large resultant wave – a big wave

Question 30

Exactly out of phase wave

Answer 30

produces a flat string

Question 31

Node

Answer 31

a point with zero amplitude

Question 32

Antinode

Answer 32

a point with a maximum amplitude

Question 33

Fixed boundary

Answer 33

reflected wave is inverted

Question 34

Free boundary

Answer 34

reflected wave is not inverted

Question 35

Resonance

Answer 35

A standing wave pattern (oscillation mode) can be produced

only for certain frequencies (resonant frequencies).

Question 36

Resonant frequency

Answer 36

L = nλ/2 where λ =2L/n
f = n(v/2L)