Question

At t = 0s, the leading edge of a wave (wavelength 1m) is 3m to the left of a boundary. The wave is moving to the right at 1m/s. The transmitted wave has wavelength 3m. (You may draw pictures to help you answer the questions below, but you must explicitly state - in words - the answers to the questions.)

(a)[8 pt(s) ]At t = 5s, where is the leading edge of the transmitted wave? Is the transmitted wave inverted or non-inverted, and why?

Answer 1

Given that the Wave has a wave length of in medium 1 and in medium 2  .it means the trasmitted wave has more wave length than the initial and reflected waves .
But the wave length is given by
        
the frequency is same for both the waves . so wave length depends on the Velocity of the waves .And the velocity is given by
   where T is the tension aand is the linear mass density(mass per unit length)
In both the strings the Tension will be same Hence the Wavelength depends on the   
   hence more the density less will be the wave length
hence medium 1 has more density that the medium 2

Given that at t=0 sec the wave is 3 m away from the boundary
speed   therefore it takes 3 seconds for the leading edge to reach the boundary

for the wave to get completely trasmitted it takes 1/f seconds.

now 4 seconds of time has completed .Now the transmitted wave will have a velocity of 3m/s and at this instant the leading edge of the transmitted wave is 3 m away (to the right) from the boundary.after i more second it travels 3 more meters
hence after 5 seconds the transmitted wave will be 6 meters away from the boundary

The transmitted wave is non - inverted because it doesn't depend on whether the wave has travelled from denser to rarer or from rarer to denser medium .It always transmits with out any phase change .But the reflected wave depends on the above condition . It inverts if the wave trveles from rarer to denser and non - inverts if travels from Denser to rarer mediums