Mechanic Waves (Textbook) - Evernote

Question 1

What is the relationship of velocity, wavelength and frequency?

Answer 1

v = λf

Question 2

What is angular frequency?

Answer 2

ω=2πf

Question 3

What is the relationship of frequency, period and angular frequency?

Answer 3

T=1/f=2π/ω

Question 4

How can y(x,t) = A·cos·[ω((x/v)-t] be rewritten? What is the relationship?

Answer 4

1. y(x,t) = A·cos·[2πf((x/v)-t]
2. y(x,t) = A·cos·[2π((x/λ)-(t/T))]
3. y(x,t) = A·cos·(kx-ωt)

Question 5

What is the wave number equation?

Answer 5

k=2π/λ

Question 6

Angular frequency has what relationship to velocity and the wave number?

Answer 6

ω=2πf=vk

Question 7

Explain why (∂²y(x,t))/∂x² = (1/v²)·((∂²y(x,t))/∂t²)?

Answer 7

Essentially done through the relationships of angular frequency to everything else and done by differentiating with respect to particular elements.

Question 8

What is the velocity for waves on a string and what does each variable mean?

Answer 8

v = √(F/μ) (waves on a string)

Question 9

What is the average power of a wave?

Answer 9

P(average) = ½√(μF)·ω²A²

Question 10

What is the inverse square law for intensity?

Answer 10

(I₁/I₂) = (r₂²/r₁²) [inverse square law for intensity]

Question 11

What is the principle of superposition and why does it work?

Answer 11

y(x,t) = y₁(x,t) + y₂(x,t) [principle of superposition]

Question 12

What is the function of a fixed standing what?

Answer 12

y(x,t) = (A{standing wave}·sin·kx)sinωt [fixed at x=0]

Question 13

The natural frequency of a wave is described how?

Answer 13

f(n) = n(v/2L)=n·f₁ (n=1, 2, 3…)

Question 14

What is the 1st natural frequency equation for a fixed string?

Answer 14

f₁ = (1/2L)·√(F/μ) [fixed both ends]