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\begin{document}

\frame{\frametitle{\b Waves I - 1} \bigskip

{\bf Transverse, travelling waves (2), (3):}
$$ y(x,t) = A\,\sin(k\,x-\omega\,t)\,.$$
Wavelength $\lambda=2\pi/k$, period $T=2\pi/\omega$, 
velocity $v$: 
$$ k\,x-\omega\,t=const~\Rightarrow~x-v\,t=\frac{const}{k}\,,
   ~~v=\frac{\omega}{k}\,. $$
\smallskip

{\bf Transverse string wave (4):} Solve
$$ v = \sqrt\frac{T}{\mu}~~{\rm for}~~T\,. $$
\smallskip

{\bf Decibel (Db) (5).} With $\beta$ given in Db the
attenuation factor is 
$$ f = 10^x~~{\rm with}~~\beta = 10\,\log_{10}(10^x)
   =10\,x\,. $$
Note that the sound level is reduced by the inverse
of this factor.
\smallskip
\vskip 20pt }


\frame{\frametitle{\b Waves I - 2} \bigskip

{\bf Stretched Spring (6):} Imagine that this spring is a rubber strap. 
With a numerical values for $v/v_0$, $n$ given, and $L_1$ known, solve
$$ \left(\frac{v}{v_0}\right) = \sqrt{\frac{\mu_0\,(n\,L_1-L_0)}
   {\mu\,(L_1-L_0)}}\,. $$
for $L_0$. Note that you also need to use the definitions of 
$\mu_0$ and $\mu$.
\vskip 20pt }
\end{document}
