Answer
(a) $\lambda = 0.439~m$
$T = 1.28~ms$
(b) $\lambda = 0.219~m$
Work Step by Step
(a) We can find the wavelength.
$\lambda~f = v$
$\lambda = \frac{v}{f}$
$\lambda = \frac{344~m/s}{784~Hz}$
$\lambda = 0.439~m$
We can find the period of oscillation.
$T = \frac{1}{f}$
$T = \frac{1}{784~Hz}$
$T = 0.00128~s = 1.28~ms$
(b) If the sound wave is one octave higher, the frequency is 1568 Hz. We can find the wavelength.
$\lambda~f = v$
$\lambda = \frac{v}{f}$
$\lambda = \frac{344~m/s}{1568~Hz}$
$\lambda = 0.219~m$
