Wave Functions:
2
y ( x, t ) = A sin ( x − vt )
x t
y ( x, t ) = A sin 2 −
T
k=
=
y = A sin (k x – ωt + φ)
2
2
T
= 2 ƒ
Speed of Waves on a String:
tension
T
=
mass/length
v=
Total Energy in one Wavelength:
Eλ= Kλ + Uλ = ½μω2A 2λ
Sound Level:
I
Io
= 10log
Threshold of pain: I = 1.00 W/m2
Threshold of hearing: I0 = 1.00 x 10-12 W/ m2
Doppler Effect:
v + vo
ƒ' =
ƒ
v − vs
Mach Angle as related to inverse Mach
Number:
vt
v
sin =
=
vst vs
Superposition of Sine Waves:
y = y1+y2 = 2A cos (φ /2) sin (kx - ωt + φ /2)
Power Associated with a Wave:
1
2 A2 1
E 2
=
=
= 2 A2v
t
T
2
Speed of Sound in Liquid or Gas:
v=
B
Speed of Sound in a Solid Rod:
Y
v=
Speed of Sound in Air at Certain Temp.:
v = (331 m/s) 1 +
TC
273 C
Sound Waves, Pressure:
ΔP = ΔPmax sin (kx – ωt)
ΔPmax = ρvωsmax
Total Energy/Power/Intensity for a Sound
Wave:
Eλ = Kλ +Uλ = ½ (ρA)ω2 smax2λ
=
I=
E E 1
=
= Av 2smax 2
t
T
2
A
Standing Wave Equation:
y = (2A sin kx) cos ωt
The wavelengths of the normal modes for a
string fixed at both ends:
λn = 2L / n n = 1, 2, 3, …
Natural Frequencies for string fixed at both
ends:
v
n T
ƒn = n
2L
=
2L
Amplitude of resultant wave of two waves with
different frequencies (beat equation):
ƒ − ƒ2
Aresultant = 2A cos2 1
t
2
0
