Examples of mechanical waves

Question 1

What is the wave speed on a taut string?

Answer 1

c^2=T/µ

Question 2

What is the transfer of power for a wave?

Answer 2

P = −T∂y/∂x ∂y/∂t
P = TA^2kω sin^2
(kx − ωt)

Question 3

What is the average power transfer for a wave?

Answer 3

Pav =1/2 ω^2A^2Z
Where Z is the impedance of the string
Z=(Tµ)^1/2

Question 4

What is the Young’s modulus?

Answer 4

Y=stress/strain

Question 5

What is the wave speed for Young’s modulus?

Answer 5

v=(Y/ρ)^1/2

Question 6

What is the wave speed for a shear wave?

Answer 6

v=(G/ρ)^1/2
Where G is the shear modulus

Question 7

What is the equation for bulk modulus?

Answer 7

B=-vdp/dV for a gas and vdp/dV for a solid

Question 8

What is the wave speed for compressive (p) waves?

Answer 8

v=((B+4G/3)/ρ)^1/2

Question 9

what is the speed of sound in an ideal gas?

Answer 9

v=(B/ρ)^1/2

Question 10

What is the equation for the Doppler effect for EM waves?

Answer 10

f’=f( (c-v)/ (c+v) )^1/2
Where v is the speed of the listener compared to the source

Question 11

What is the equation for the Doppler effect for sound waves?

Answer 11

f’=f( (c+u_0)/ (c+u_s) )^1/2
Where u_0 is the speed of the listener and u_s is the speed of the source