5-58 Equation Reference
Variable
Description
sm
Longitudinal amplitude
t
Time
v
Speed of sound in medium (Sound Waves),
or Wave speed (Transverse Waves,
Longitudinal Waves)
x
Position
y
Transverse displacement at x and t
ym
Transverse amplitude
Reference: 3.
Transverse Waves (15,1)
Equations:
Example:
Given: ym=6.37_cm, k=32.11_r/cm, x=.03_cm,
ω
=7000_r/s, t=1_s.
Solution: f= 1114.0846_Hz,
λ=0.0020_cm, y=2.6655_cm, v=218.0006_cm/s.
Longitudinal Waves (15, 2)
Equations:
Example:
Given: sm=6.37_cm, k=32.11_r/cm, x=0.03_cm,
ω
=7000_r/s, t=1_s.
Solution: s=5.7855_cm, v=2.1800_m/s,
λ=0.1957_cm, f=1114.08456_Hz.
Sound Waves (15, 3)
Equations:
Example:
Given: sm=10_cm,
ω
=6000_r/s, B=12500_kPa,
ρ
=65_kg/m^3.
Solution: v=438.5290_m/s, I=5130789412.97_W/m^2,
β
=217.018_dB, f=954.9297_Hz.
y y m S I
k
⋅
ω
t
⋅
( ) ⋅
=
v
λ
⋅
=
k
2
π⋅
λ
----------
=
ω
2
π
⋅ ⋅
=
s s m C O S k x
⋅
ω
t
⋅
( ) ⋅
=
v
λ
⋅
=
k
2
π⋅
λ
----------
=
ω
2
π
⋅ ⋅
=
v
B
- - - - =
I
1
2
- - -
ρ
v
ω
2
sm
2
⋅ ⋅ ⋅ ⋅
=
β
10 LO G
I
10
- - - - - -
⋅
=
ω
2
π
⋅ ⋅
=
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Weight and Dimensions
