2. Sound Waves?
• Longitudinal waves that create
regions of high and low
pressure as they displace
molecules in a medium.
3. Equations
• Bulk modulus
numeral constant that describes how much fraction of the volume of a
medium changes as pressure changes.
How “elastic” the medium is.
• Speed of Sound
4. Problem 1
• You are an aquatic organism that plays the guitar.
a) What would be the speed of sound from the guitar
underwater (the temperature is 20 ºC)? Does the pitch
(frequency) of your guitar affect the speed?
b) How fast would the sound travel if you were to play on
land (the temperature is 20 ºC)?
c) Where does sound travel faster? Underwater or on land?
d) How fast would sound travel if you were to play in a
vacuum?
5. Solution 1
a) Using the formula v = √𝐵/𝑝, you get v = √(Bulk modulus of water)/(Density of water).
Therefore, the answer is v = √(2.2* 109 pa)/(1000 kg/m3) = 1.48* 103 m/s. The speed of
sound does not depend on its frequency.
b) v = √(Bulk modulus of air)/(Density of air) = √(1.01* 105 pa)/(1.2 kg/m3) = 2.9 * 102 m/s.
However, this is incorrect since the compression and rarefaction of air caused by sound
wave is fast. It is so that heat does not have enough time to be transferred, causing the
bulk modulus to increase. The observed speed of sound is close to 343 m/s.
c) Although water is denser than air, sound travels faster in water.
d) 0 m/s, since there aren’t any medium for the sound to propagate!
6. Sound Intensity
• Given by the equation
• Often expressed in decibels (dB), a logarithmic unit where 0 dB
equals to an intensity I0= 10-12 W/m2.
• Decibels are expressed using the equation
7. Problem 2
• A robot emits a sound wave that has frequency of 4800 Hz and you, an aquatic creature
detect it (underwater).
a) Assuming that the displacement of the sound is 1.0*10
−11 m, how intense is the sound
emitted by the robot.
b) Express how intense the sound would be in decibels if you were to detect it on land.
c) How much more intense is 50 dB sound compared to 0 dB sound?
8. Solution 2
a) Use the equation I = ½ 𝑝𝑣ω2 𝑠m. I = ½ (1000 kg/m3)(1482
m/s)(2π)2(4800s
−1)2(1.0*10
−11 m)2 = 6.74*10
− 𝟖 W/m2.
b) Use the equation β(I) = 0 dB + 10 log10(I/I0). β(I) = 0 dB + 10
log10[(6.74*10
−8 W/m2)/ (10-12 W/m2)] = 48.29 dB.
c) Intensity increases tenfold every 10 dB. Therefore, 50 dB is
100000 times more intense than 0 dB.
