Waves

Question 1

Mechanical waves

Answer 1

Mechanical wave is a type of wave that obeys Newton’s laws and needs a material. I.e wave on a string, sound wave, water wave

Question 2

Transverse wave

Answer 2

A wave that shifts the whole string up and down

Y = Ym sin (wt)

Vertical motion = Amplitude * sin(angular frequency * time)

Question 3

Longitudinal wave

Answer 3

A wave that shifts from side to side. Imagine tugging on a spring and letting it go. This type of wave has compressions and refractions in it.

Question 4

Velocity of propagation

Answer 4

The velocity of a particle moving forward

Types:
transversal on a string
longitudinal in a solid
longitudinal in a gas or a liquid

Question 5

Velocity of a particle

Answer 5

In a sine wave the particle moves up and down with this velocity

square root of modulus of elasticity to density ratio

Question 6

Transveral velocity on a string

Answer 6

square root of tension [N] to linear density [kg/m] ratio

Question 7

Longitudinal velocity in a solid body

Answer 7

square root of modulus of elasticity [Pa] to material density [kg/m^3] ratio

Question 8

Longitudinal velocity in a gas or a liquid

Answer 8

square root of bulk modulus [Pa] to density [kg/m^3] ratio

Question 9

Wave number

Answer 9

K = 2pi/wavelength [m^-1]

Question 10

Angular frequency

Answer 10

W = 2pi/ period, W = 2pi * frequency [s^-1]

Question 11

Wave equation

Answer 11

Y = amplitude * sin (kw - wt) when travelling to the right 
Y = amplitude * sin (kw + wt) when tavelling to the left

Question 12

Velocity

Answer 12

V = angular frequency / wave number if its to the right 
V = - angular frequency / wave number if its to the left

OR

V = wavelength / period = wavelength * frequency

Question 13

Particle velocity and acceleration, one dimensional wave

Answer 13

v = d(ym sin (kx - wt ))/dt (first derivative of the displacement function)

a = dv/dt (second derivative of the displacement function)

Question 14

Particle velocity and acceleration, one dimensional wave (learn derivation later)

Answer 14

v = d(ym sin (kx - wt ))/dt (first derivative of the displacement function)

wym = amplitude of particle velocity

a = dv/dt (second derivative of the displacement function)

Question 15

Wave equation in one dimension

Answer 15

second derivative of y by x = (1/velocity^2) * second derivative of y by t

Question 16

Wave equation in three dimensions

Question 17

Wave interference

Answer 17

Constructive and destructive

Question 18

Standing waves

Answer 18

Some particular points of this wave are fixed and other moves. Example: a fixed string.
Equation: y = 2ym sin (kx) cos (wt)

Nodes - points at zero amplitude
Antinodes - points at max amplitude

POSITION OF NODES EQUATION, K VALUES
DISTANCE BETWEEN THE NODES

Question 19

Energy

Answer 19

2 pi^2 frequency^2 density area speed time amplitude^2

Question 20

Average power

Answer 20

Energy / t

Question 21

Average power

Answer 21

Energy / t

Question 22

Intensity of a wave

Answer 22

Power per unit area or Energy per (unit area * time)

Question 23

Wave equation with wave constant

Answer 23

y = ym sin (kx - wt + phase constant [rad])

Question 24

What is fundamental frequency. What are wave number and position for nodes and antinodes

Answer 24

The fundamental frequency is the lowest frequency for starting a standing wave.

For nodes:
wave number 0,pi,2pi
position pi n/2

For antinodes:
wave number pi/2,3pi/2 etc
position (n+1/2) lambda/2