The displacement of a wave can be described by the equation:?

Question

y = a sin(t -kx + )

Give the name and meaning of each symbol, and show how the frequency, wavelength, and velocity can be deduced from this equation. [30%]

Derive the Doppler shift equation:

for a sound source that is moving towards a fixed detector at velocity vs . (fo is an emitted frequency, fa is the apparent frequency, and c is the speed of sound) . [40%]

In many applications waves are transmitted from a stationary source, and reflected back by a moving object. State one such application, and write down an expression (in terms of the velocity of the moving reflector) for the frequency shift that will be detected. [30%]

Answer 1

y = Asin(ωt - kv + φ)
f = ω/(2π)
v = 1/k