waves

Question 1

transverse wave

Answer 1

elements move perpendicular to direction of propagation

Question 2

longitudinal wave

Answer 2

elements move parallel to direction of propagation

Question 3

y(x,t) for sinusoidal wave

Answer 3

y(x,t) = A sin[(2π/λ)(x - vt)]

Question 4

velocity of wave

Answer 4

v = λf

Question 5

wave number

Answer 5

k = 2π/λ

Question 6

angular frequency

Answer 6

ω = 2π/T

Question 7

wave max velocity

Answer 7

v_max = ωA

Question 8

wave max acceleration

Answer 8

a_max = ω²A

Question 9

speed of waves on string

Answer 9

v = √(T/μ)

• T -> Tension*
• μ -> mass per unit length*

Question 10

rate of energy transfer in sinusoidal wave

Answer 10

P = 1/2(μω²A²v)

Question 11

general linear wave equation

Answer 11

∂²y/∂x² = (1/v2)∂²y/∂t²

Question 12

speed of sound in medium

Answer 12

v = √(B/ρ)

B -> bulk modulus of material

Question 13

Pressure variation in sound wave

Answer 13

ΔP = ΔP_maxsin(kx-ωt)

Question 14

max pressure in sound wave

Answer 14

ΔP_max= ρvωs_max

Question 15

Intensity of wave (general)

Answer 15

I = P/A

Question 16

intensity of sound wave

Answer 16

I = 1/2ρv(ωs_max)²= ΔP²_max/2ρv

Question 17

intensity of spherical wave

Answer 17

I = P_avg/4πr²

Question 18

sound level in decibals

Answer 18

β = 10 log(I/I₀)

I₀ -> reference intensity

Question 19

frequency of sound with observer moving towards source

Answer 19

f’ = f(v+v_o)/v

• v_o -> velocity of observer*
• speed of sound remains constant, wavelength and frequency change*

Question 20

frequency of sound with observer moving away from source

Answer 20

f’ = f(v - v_o)/v

Question 21

doppler shift

Answer 21

f’ = f(v + v₀)/(v - v_s)

moving closer -> increases frequency
moving apart -> decreases frequency

Question 22

mach angle

Answer 22

sinθ = v/v_s

Question 23

wave function of standing wave

Answer 23

y = (2Asin(kx))cos(ωt)

Question 24

distance/definition between antinodes

Answer 24

antinodes are points of maximum displacement
distance is λ/2

Question 25

distance between nodes

Answer 25

nodes are points of 0 displacement
distance between nodes is λ/2

Question 26

distance between node and antinode

Answer 26

λ/4

Question 27

frequency of standing wave in string

Answer 27

f_n = n/(2L)√(T/ μ)

Question 28

wavelength of standing wave in string

Answer 28

λ_n = 2L/n

Question 29

node or antinode at open end of pipe?

Answer 29

antinode

Question 30

node or antinode at closed end of pipe?

Answer 30

node

Question 31

natural frequency of pipe open at bothe ends

Answer 31

f_n = nv/2L

v -> speed of sound in air

Question 32

natural frequency of pipes closed at one end, open at another

Answer 32

f_n = nv/4L

Question 33

beat frequency of 2 sound waves

Answer 33

f_beat = |f₁ - f₂|