Hifumi's Study Notesnotesphysicscegep3sound

sound

Tags

phys/wave

cegep/3

Word count

240 words

Reading time

2 minutes

Longitudinal mechanical wave that consists of compressions and rarefactions of the medium

Travelling speed in air at 20°C is == $243 m / s$ ==.
Travels faster at higher temperatures
Human audible frequency: 20-20000Hz

Intensity

Measured in decibels:

β = 10 dB \log \frac{I}{I_{o}}

Human audible intensity: $I_{o} = 10^{- 12}$ to $1 W / m^{2}$
Low frequencies correspond to lower pitch, high frequencies correspond to higher pitch

Examples

A loudspeaker suspended high off the ground emits 35.0 J of energy per second, with a uniform distribution in all directions. A small detector is located 55.0 m from the speaker.

What is the sound intensity at the detector’s position?

\begin{aligned} I & = \frac{P}{4 π r^{2}} \\ = \frac{35}{4 π \cdot 55^{2}} \\ \approx 0.009087 W / m^{2} \end{aligned}

How much energy will be transferred to the detector in 60 seconds, if the detector has a surface area of 0.01 $m^{2}$ ?

\begin{aligned} E & = I t S \\ = 0.009087 \cdot 60 \cdot 0.01 \\ \approx 0.005452 J \end{aligned}

The sound intensity level from one solo flute is 70 dB. If 100 identical flutists standing close together play in unison, what will be the sound intensity level?

\begin{aligned} β_{i} & = 10 \log \frac{I_{i}}{I_{o}} \\ 70 & = 10 \log \frac{I_{i}}{I_{o}} \\ 10^{7} & = \frac{I_{i}}{I_{o}} \\ I_{i} & = 10^{- 5} W / m^{2} \\ β_{f} & = 10 \log \frac{I_{f}}{I_{o}} \\ = 10 \log \frac{100 \cdot 10^{- 5}}{I_{o}} \\ = 10 \log 10^{9} \\ = 90 dB \end{aligned}

Contributors

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