Longitudinal and Transverse waves

v = \frac{E}{d}

where $E$ is the appropriate modulus and $d$ is the density. For a rod, $E$ is the Young’s modulus; for a fluid $E$ is the Bulk modulus.

Wave Motions

Velocity of wave = \frac{distance travelled by wave}{time taken}

⟹ \frac{number of waves \times wave length}{time}

v e l oc i t y = f re q u e n cy \times w a v e l e n g t h

v = nλ

if $v_{t}$ and $v_{o}$ are the velocities of sound at $t \celsius$ and $0 \celsius$ respectively,
then

\frac{v _{t}}{v _{0}} = \frac{T _{t}}{T _{0}}

where $T_{t}$ and $T_{0}$ are the absolute temperatures.

Note

absolute temperature require you to convert to Kelvin scale.

I = 2 π^{2} f^{2} a^{2} v d

where, $f = f re q u e n cy$
$a = am pl i t u d e$
$v = velocty of the wave$
$d = density of the medium$

If $P$ is the power of an isotopic source of sound at a distance $r$ , the intensity or loudness of sound.

I = \frac{P}{4 π r ^{2}}

MTTF = \frac{Total operating time of all units}{Total number of failures}

MTBF = \frac{Total operating time (uptime)}{Number of Failures}

λ = \frac{1}{MTBF}

A \approx \frac{MTBF}{MTBF + MTTR}

where $MTTR$ is mean time to repair.