Solved: When a transverse sinusoidal wave is present on a

QUESTION:

When a transverse sinusoidal wave is present on a string, the particles of the string undergo SHM. This is the same motion as that of a mass attached to an ideal spring of force constant \(k^{\prime}\), for which the angular frequency of oscillation was found in Chapter 14 to be \(\omega=\sqrt{k / m}\). Consider a string with tension  and mass per unit length \(\mu\), along which is propagating a sinusoidal wave with amplitude A and wavelength \(\lambda\). (a) Find the “force constant” \(k^{\prime}\) of the restoring force that acts on a short segment of the string of length \(\Delta x) (where \(\Delta x \ll \lambda\)). (b) How does the “force constant” calculated in part (b) depend on , \(\mu\), , and \(\lambda\)? Explain the physical reasons this should be so.

Equation Transcription:

Text Transcription:

K’

omega=sqrtk/m

U

Lambda

K’

Deltax

deltax<<lambda

U

Lambda