You have two string segments of equal length. Segment 1 has linear mass density M₁and segment 2 has linear mass density µ₂. You splice the two together and then tie the combination tautly between two posts. You've spliced in such a way that, once attached to the posts, the length of segment 1 to the left of the splice is the same as the length of segment 2 to the right of the splice. When you pluck at a particular frequency you set up a standing wave that has this pattern: nodes at the splice and where each segment is attached to its pole, plus m more nodes in segment 1 and n more nodes in segment 2. a) What is the numerical value of ¹? (Be sure to draw a number of diagrams with μ₂ a few different values of m and n so that you can see the pattern for different m and n values on the wavelengths.) M₁_ £ H₂ b) If μ₂ > μ₁, is m or n bigger? (Which segment has more nodes.)

You have two string segments of equal length. Segment 1 has linear mass density M₁and segment 2 has linear mass density µ₂. You splice the two together and then tie the combination tautly between two posts. You've spliced in such a way that, once attached to the posts, the length of segment 1 to the left of the splice is the same as the length of segment 2 to the right of the splice. When you pluck at a particular frequency you set up a standing wave that has this pattern: nodes at the splice and where each segment is attached to its pole, plus m more nodes in segment 1 and n more nodes in segment 2. a) What is the numerical value of ¹? (Be sure to draw a number of diagrams with μ₂ a few different values of m and n so that you can see the pattern for different m and n values on the wavelengths.) M₁_ £ H₂ b) If μ₂ > μ₁, is m or n bigger? (Which segment has more nodes.)