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Question
A string of mass 2.5 kg is under a tension of 200 N. The length of the stretched string is 20.0 m. If the transverse jerk is struck at one end of the string, the disturbance will reach the other end in ______.
Options
one second
0.5 second
2 seconds
data given is insufficient
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Solution
A string of mass 2.5 kg is under a tension of 200 N. The length of the stretched string is 20.0 m. If the transverse jerk is struck at one end of the string, the disturbance will reach the other end in 0.5 second.
Explanation:
Mass m = 2.5 kg
μ = Mass per unit length
= `m/l`
= `(2.5 kg)/20`
= `125/10`
= 0.125 kg/m
Speed `v = sqrt(T/μ)`
= `sqrt(200/0.125)` ......[Speed of transverse waves in any string]
`l = v xx t`
⇒ `20 = sqrt(200/0.125) xx t`
⇒ `t = 20 xx sqrt(125/(2 xx 10^5)`
= `20 xx sqrt((25 xx 5)/(2 xx 10^5))`
= `20 xx sqrt(25 xx 1/(0.4 xx 10^5))`
= `20 xx 5 sqrt(1/(4 xx 10^4))`
= `(20 xx 5)/(2 xx 10^2)`
= `1/2`
= 0.5
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