A string of mass 2.5 kg is under tension of 200 N. The length of the stretched string is 20.0

step 1 Dear students, in problem 146 of chapter 9, wave and oscillations and wave, we've asked that a s

A string of mass 2.5 kg is under tension of 200 N. The...

A string of mass $2.5 \mathrm{~kg}$ is under tension of $200 \mathrm{~N}$. The length of the stretched string is $20.0 \mathrm{~m}$. If the transverse jerk is struck at one end of the string, the disturbance will reach the other end in (A) $1 \mathrm{~s}$ (B) $0.5 \mathrm{~s}$ (C) $2 \mathrm{~s}$ (D) Data given is insufficient

A string of mass $2.5 \mathrm{~kg}$ is under tension of $200 \mathrm{~N}$. The length of the stretched string is $20.0 \mathrm{~m}$. If the transverse jerk is struck at one end of the string, the disturbance will reach the other end in
(A) $1 \mathrm{~s}$
(B) $0.5 \mathrm{~s}$
(C) $2 \mathrm{~s}$
(D) Data given is insufficient

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Key Concepts

Relationship Between Speed, Distance, and Time

This fundamental relationship states that the time it takes for a disturbance to travel through a medium is equal to the distance divided by the speed of the wave. Knowing any two of these quantities allows you to calculate the third, which is essential for analyzing the propagation of waves along a string.

Wave Speed on a String

This concept explains that the speed at which a wave travels along a string is determined by the tension in the string and its linear mass density. The relationship is given by the formula v = ?(T/?), where v is the speed, T is the tension, and ? is the mass per unit length. This formula shows that increasing the tension or decreasing the mass per unit length will result in a faster wave propagation.

Linear Mass Density

Linear mass density is a measure of how much mass is distributed per unit length along the string, typically denoted by ?. It plays a crucial role in determining how the string reacts to forces and how quickly disturbances can travel through it. A lower linear mass density means the string will accelerate faster under a given tension.

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