Answer
(a) The wavelength decreases.
(b) The frequency increases.
(c) The time for a pulse to travel the length of the string decreases.
(d) The maximum velocity of a point on the string increases.
(e) The maximum acceleration of a point on the string increases.
Work Step by Step
(a) $\lambda = 2L$
If the length decreases, then the wavelength decreases.
(b) $f = \frac{v}{\lambda}$
Since the wave speed stays the same while the wavelength decreases, the frequency increases.
(c) Since the wave speed stays the same while the total distance decreases, the time for a pulse to travel the length of the string decreases.
(d) $v_m = A~\omega$
$v_m = A~(2\pi~f)$
Since the frequency increases, the maximum velocity of a point on the string increases.
(e) $a_m = A~\omega^2$
$a_m = A~(2\pi~f)^2$
Since the frequency increases, the maximum acceleration of a point on the string increases.
