Case 3, the junction lies at some other position: d. d. Case 3 Derivation: Let x = 0 at the interface. Write an equation for a standing wave for x>0 and x < 0. Note there are two wave numbers, k+ and k- but there is only one w. Use the boundary condition that y+ = y- and y'+ = y'- at x = 0 to obtain a relation between the two amplitudes, A+ and A- and the wavenumbers k+ and k- and the offsets d+ and d-.
In this question you have setup standing waves on mismatched string and compare the amplitudes of waves the light and heavy string. The relation between the amplitudes depends on where the junction lies with respect to nodes and antinodes.
Case 3, the junction lies at some other position ( In other words x=0 does NOT start at a node or anitnode)
Let x = 0 at the interface. Derive and write an equation for a standing wave for x >0 and x<0. Note there are two wave numbers, k+ and k. but there is only one ω. Use the boundary condition that y+ = y- and y'+ = y'- at x = 0 to obtain a relation between the two amplitudes, A+and A- and the wavenumbers k+ and k- and the offsets d+ and d-.
Trending now
This is a popular solution!
Step by step
Solved in 5 steps with 5 images
