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MODULE 6: SOUND WAVES
Part 1: Sound Intensity and Intensity Level
1. During a typical workday (eight hours), the average sound intensity arriving at Larry’s ear is about
1.80 × 10–5 W/m2. The area of Larry’s ear through which the sound passes is 2.10 × 10–3 m2
a) What is the power entering each of Larry’s ears during the workday?
b) What is the total energy entering each of Larry’s ears during the workday?
c) Larry would like to move far away from a loud coworker so that the sound intensity Larry
experiences decreases to one-fourth its original value. What is the ratio of Larry’s distance after
he moved (𝑟far ) to before he moved away from the coworker (𝑟near)?
𝑟far
=
𝑟near
d) If 5 coworkers are each talking loudly with an intensity of 1 × 10–7 W/m2, what is the total sound
level in decibels (dB) that Larry experiences?
PHY-124 Module 6 Recitation (Sound Waves)
e) Larry goes to the break room and stands at point B near two speakers, S1 and S2, shown below in
a top-down view of the room. The speakers emit sound at a frequency of 170 Hz in-phase with
one-another, and the speed of sound is 340 m/s. As Larry stands at point B, does he hear
amplified (loud) sound, or relatively quiet sound?
Part 2: Boundary Conditions in Standing Waves
2. There are two types of boundary conditions for pipes: closed ends and open ends. Some instruments
are pipes open at one end and closed at the other, others are open at both ends.
a) Should there be a node or an antinode at the open end? What about at the closed end? What does
the node and antinode represent: pressure, or particle displacement?
b) Fill in the table below by sketching the first three harmonics (sound-producing situations) for the
two types of boundary conditions typically found with air columns (pipes). The first one is done
for you.
Both ends open
n=1
n(L)
1=2L
One end open/one end closed
n=1
n=2
n=2
n=3
n=3
n(L)
1=4L
PHY-124 Module 6 Recitation (Sound Waves)
c) Given that 𝐿1 = 𝜆1 /4 for one end open one end closed, why is the next audible harmonic
correspond to n=3 and not n=2 (based on the diagram you drew)?
d) Describe what is physically happening in the air at a node and at an antinode. (Hint: see this
animation a visual: https://www.acs.psu.edu/drussell/Demos/StandingWaves/standing.gif)
Part 3: Standing Waves in an Air Column
3. A child blows air over the top opening of an empty bottle, and the bottle resonates at a fundamental
frequency of 710.0 Hz. The speed of sound in air is 340 m/s.
a) Make a sketch of the standing sound wave inside the bottle for the fundamental frequency, clearly
showing the locations of nodes and antinodes.
b) What is the length of the bottle?
c) What is the frequency of the next audible harmonic of this bottle?
PHY-124 Module 6 Recitation (Sound Waves)
d) The child cuts open the bottom of the same bottle and now it is open at both ends, assume that the
length of the bottle does not significantly change. Make a sketch of the fundamental standing
wave in the bottle with both ends open.
e) Determine the new fundamental frequency of the bottle.
f) What is the frequency of the next audible harmonic in this case with both ends
now open?