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Solved: CALC Speed of Propagation vs. Particle Speed. (a)
Chapter 15, Problem 12E(choose chapter or problem)
Speed of Propagation vs. Particle Speed. (a) Show that Eq. (15.3) may be written as
\(y(x, t)=A \cos \left[\frac{2 \pi}{\gamma}(x-v t)\right]\)
(b) Use \(y(x,t)\) to find an expression for the transverse velocity \(v_{y}\) of a particle in the string on which the wave travels.
(c) Find the maximum speed of a particle of the string. Under what circumstances is this equal to the propagation speed \(v\)? Less than \(v\)?Greater than \(v\)?
Questions & Answers
QUESTION:
Speed of Propagation vs. Particle Speed. (a) Show that Eq. (15.3) may be written as
\(y(x, t)=A \cos \left[\frac{2 \pi}{\gamma}(x-v t)\right]\)
(b) Use \(y(x,t)\) to find an expression for the transverse velocity \(v_{y}\) of a particle in the string on which the wave travels.
(c) Find the maximum speed of a particle of the string. Under what circumstances is this equal to the propagation speed \(v\)? Less than \(v\)?Greater than \(v\)?
ANSWER:
Solution 12E
Equation 15.3 is given as,
(a) Let us simplify this equation.
(since
)
(since wavelength
) …..(1)