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A string of length 40 cm and weighing 10...

A string of length 40 cm and weighing 10 g is attached to a spring at one end and to a fixed wall at the other end. The spring has a spring constant of `160 N m^-1` and is stretched by 1.0 cm. If a wave pulse is produced on the string near the wall, how much time will it take to reach the spring ?

Text Solution

Verified by Experts

`L=40 cm, mass=10 g`
mass per unit length
`mu=(10)/(40)=(1)/(4)(g//cm)`
spring constant `k=160 N//m`
deflection, `x=1 cm=0.01 m`
tension in the string:
` T=kx=160xx0.01=1.6 N`
`=16xx10^(4)"dyne"`
wave velocity is given by
`v=sqrt(((t)/(mu)))=sqrt((((16xx10^(4)))/((1)/(4))))=800 cm//s`
Time taken by the pulse to reach the spring
`t=(40)/(800)=(1)/(20)=0.05 s=5xx10^(-2)s`.
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