Waves at boundaries and standing waves

Question 1

What is the boundary condition for a free end?

Answer 1

(∂y/∂x)= 0
At x0

Question 2

What happens to the wave at an end?

Answer 2

It is reflected and inverted

Question 3

What is the wave speed for two strings joined together?

Answer 3

v =(T/µ)^1/2

Question 4

What is the form of the incident wave?

Answer 4

yi(x, t) = Ai cos(k1x − ωt)

Question 5

What is the form of the reflected wave?

Answer 5

yr (x, t) = Ar cos(−k1x− ωt)

Question 6

What is the form of the transmitted wave?

Answer 6

yt(x, t) = At cos(k2x −ωt)

Question 7

What are the boundary conditions for two strings joined together?

Answer 7

y_i+y_r=y_t
∂y_i/∂x+∂y_r/∂x=∂y_t/∂x as the tension is the same in both strings
All at x0

Question 8

What is the transmission coefficient?

Answer 8

t = At/Ai= 2Z1/(Z1 + Z2)

Question 9

What is the reflection coefficient?

Answer 9

r = Ar/Ai= (Z1 − Z2)/(Z1 + Z2)

Question 10

What happens when µ1<µ2?

Answer 10

The reflected wave is inverted and the transmitted wave is normal

Question 11

What happens when µ1>µ2?

Answer 11

The reflected wave is normal and the transmitted wave is normal

Question 12

What happens when µ1=µ2?

Answer 12

The reflected wave is not there and the transmitted wave is normal

Question 13

What happens to Power at the boundary?

Answer 13

Pi=Pr+Pt

Question 14

What is the equation for wavelength for a standing wave?

Answer 14

λ = 2L/n

Question 15

What is the equation for frequency for a standing wave?

Answer 15

f = nv/2L