Chapter 15 - Mechanical Waves Flashcards
What is a wave?
Any disturbance that propagates from one region to another.
A mechanical wave travels within some material known as the
Medium
Amplitude A is:
The maximum displacement of a particle in the medium.
What is a sinusoidal wave?
A special periodic wave in which each point moves in SHM.
The wave function y(x,t) describes:
The displacements on individual particles in the medium.
Wave equation for a sinusoidal wave travelling in the +x direction
=Acos(omega(x/v - t))
=Acos2pi(x/lambda - t/T)
=Acos(kx-omegat)
If a wave is moving in the -x direction, the wave equation changes how?
Minus signs become positive
K =
2pi/lambda
Omega
=2pif=vk
The speed of transverse waves on a string depends on what?
Tension F and mass per unit length Inertia U
V= SQRT(F/u)
Dy/dx y(x,t)
-kAsin(kx-omegat)
Slope
D^2y/dx^2 y(x,t)
-k^2Acos(kx-omegat)
Curvature
The wave equation:
Curvature= 1/v^2 d^2y(x,t)/dt^2
U
M/L
Inertia
Average power
= 0.5 SQRT(inertiaF)omega^2A^2
For waves that spread out in R3 the wave intensity is inversely proportional to:
The square of the distance from the source.
I1/I2=r2^2/r1^2
Principle of superposition:
Y(x,t) = y1(x,t) + y2(x,t)
When a sinusoidal wave is reflected from a fixed or free end of a stretched string:
The incident and reflected waves combine to form a standing wave with nodes and antinodes.
Adjacent nodes and antinodes are respectively spaced how far apart?
Lambda/2
Y(x,t) for a standing wave on a string where x=0
(Asinkx)sin(omegat)
fn=
n(v/2L)=nf1
Fundamental frequency
1/2L SQRT(F/inertia)
