Wave propagation in composite string · CAP 2005 #16

Physics

Problem

A string of length

L

is composed of two segments of equal length. One segment has linear mass density

\rho_1

and the other

\rho_2 \neq \rho_1

. One segment is tied to a wall, and the string is stretched by a force, applied to the other segment, which is much greater than the total weight of the string. If

T_i

is the tension in the

i

th segment, and

v_i

the speed of a transverse wave propagating along that segment, (a)

v_1 = v_2

and

T_1 = T_2

; (b)

v_1 \neq v_2

and

T_1 = T_2

; (c)

v_1 = v_2

and

T_1 \neq T_2

; (d)

v_1 \neq v_2

and

T_1 \neq T_2

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