Waves

Question 1

what is a wave

Answer 1

a collective bulk disturbance that propagates through a medium, in which whatever happens at any specific point is a delayed response to the disturbance at adjacent points

Question 2

the wave carries only

Answer 2

energy as it has no net displacement

Question 3

you get a wave if and only if

Answer 3

there is finite speed of propagation of the forces that move the disturbance

Question 4

Transverse waves on a string

Answer 4

wiggle one end and a pulse moves along the string

Question 5

what determines the propagation speed of the pulse

Answer 5

tension in the string and the string’s mass density

Question 6

the wave speed will increase if

Answer 6

the forces/tension are higher
or
the mass density is lower

Question 7

c² ∝

Answer 7

T/ρ

Question 8

The element does not move along the string, only moves

Answer 8

transversely as pulse propogates

Question 9

The wave equation

Answer 9

derived from the net force of the transverse forces = ma

δ²y/δx²= ρ/T * δ²y/δt²

Question 10

superposition

Answer 10

if we have solutions y₁(x,t) and y₂(x,t) then any combination Ay₁(x,t) ± By₂(x,t) will also be a solution

Question 11

The kinetic energy in a travelling wave

Answer 11

Ek = 1/2δmv^2 = 1/2 ρ *δx *(δy/δt)²

Question 12

The potential energy in a travelling wave

Answer 12

Ep = Tδx/2 (δy/δx)²

Question 13

δy/δt = dy/du =

Answer 13

-c δy/δx

Question 14

Total energy for once cycle

Answer 14

E = 1/2ρA²ω²λ

Question 15

Power formula

Answer 15

P = 1/2A²ω²√Tρ

Question 16

boundary
- free to move

Answer 16

restoring force is zero
reflected wave has same polarity (no phase change) as incident wave

Question 17

boundary
- fixed

Answer 17

displacement is zero
reflected wave has inverted polarity

Question 18

counter-propagating waves definition

Answer 18

sine waves travelling in opposite directions create standing waves when they meet

each element of the string appears to execute - synchronously - the same transverse motion

Question 19

counter-propagating waves mathematically described

Answer 19

y(x,t) = X(x)T(t)

Question 20

A standing wave is equivalent to

Answer 20

the sum of two counter-propagating travelling waves of the same frequency and amplitude

Question 21

energy densities

Answer 21

energy density = ρ/2(∂y/∂t)^2 + T/2 (∂y/∂t)^2

the energy divided by the unit length δx.

Question 22

deriving the wave equation

Answer 22

F = ma

T [∂y/∂x |xo+∂x/2 - ∂y/∂x | xo - ∂x/2 ] = ρdx ∂^2y/∂t^2 | xo

T ∂^2y/∂x^2 | xo = ρ ∂^2y/∂t^2

Question 23

how to derive kinetic Eone cycle

Answer 23

take the transverse wave y(x) = A cos(kx-wt)

K = 1/2 (λ ∫ 0) (dy/dt)^2 p x dx

similar for U.