Question

A uniform string of length 20 m and mass 1 kg is hung vertically. Find the speed of wave at the mid point of the string.
(1) 20 m/s (2) 30 m/s (3) 10√2 m/s (4) 10 m/s

Answer 1

answer : option (4) 10 m/s

explanation : linear mass density , μ = mass of string/length of string = m/l = 1/20 = 0.05 kg/m

tension at x height from the bottom of the string is T = (m/l)gx = μgx

speed of wave at x distance from the bottom of the string is given as v = √{T/μ}

= √{μgx/μ}

= √(gx)

we have to find the speed of wave at the midpoint of the string.

so, x = 10m and g = 10m/s²

then, v = √(10 × 10) = 10 m/s

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Answer 2

$\huge\bold\purple{Answer:-}$

(4) 10 m/s