Sound
Review
True or False?
• 1. The transverse waves on a vibrating
string are different from sound waves.
• 2. Sound waves are longitudinal pressure
waves.
• 3. Light travels very much slower than
sound.
• 4. Sound can travel through vacuum.
• 5. "Pitch" (in music) and frequency have
approximately the same meaning.
• 6. Decibels are related to sound intensity.
What are beat frequencies?
• The difference in pitch between 2
frequencies. (No beats indicate the
frequencies are the same.)
• fb = f1 – f2
• Example: If two piano strings had
frequencies of 529 Hz and 534 Hz what
would the beat frequency be?
• 534 – 529 = 5 Hz
Another example:
• What if a 346 tone is played and a
beat frequency of 4 Hz is heard.
What is the frequency of the other
tone?
• Either 350 or 342 Hz.
What do decibels measure?
• Intensity level (loudness).
• A sound twice as loud has 10 times the
intensity.
• A log scale is used. β = 10dB log (I/Io)
• Difference in the decibel levels of the
two sounds is β = 10dB log (I2/I1)
How is intensity measured?
• I = P/A
• At a distance of 3.8 m from a siren, the
sound intensity is 3.6 x 10-2 W/m2.
Assuming that the siren radiates sound
uniformly in all directions, find the
total power radiated.
• P = 4πr2I = Energy/time
• P = 6.5 W
Linear Density
• A uniform wire carries waves whose
frequency and wavelength are 450Hz and
1.2 m respectively. If the string is known to
be under a tension of 250 N, what is the
linear density of the wire?
• Use m/L = F/v2.
• V is found using v = λf, v=540 m/s, so
• μ = m/L = 8.57 x 10-4 kg/m.
Some Vocabulary
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Mach?
Faster than the speed of sound
Doppler?
Change in frequency due to motion of the source or
observer.
Superposition?
Sound is the sum of all the sound waves.
Interference?
Constructive and Destructive
Ultrasound?
Outside upper range of human hearing.
Superposition/Interference
• Two pulses of identical shape travel toward each other in
opposite direction on a string as shown in the figure.
• Which one of the following statements concerning this
situation is true?
• A) The pulses will reflect from each other.
• B) The pulses will interfere to produce a standing wave.
• C) The pulses will pass through each other and produce
beats.
• D) As the pulses pass through each other they will cancel
each other out.
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Examples of an Open Pipe?
Trumpet, trombone, sax, flute
Closed pipe?
Organ
Harmonics – f1, f2, f3…
• What’s the fundamental frequency?
• f1
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Which have all harmonics?
Open/open and fixed string
Which have only odd?
Open/closed
Which have only even?
None
Example:
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If f1 is 260 Hz, what is f2?
520 Hz
f3?
780 Hz
f4?
1040 Hz
The lowest note one type of flute
can produce with all the holes
closed is a “C” note with a
fundamental frequency of
261.6Hz. Flutes are an open tube.
How long should the distance be
from the mouthpiece to the end to
make this sound?
Use v = 343 m/s
Solution
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Use n = 1
f = v/(2L).  L = ?
L = v/(2f1)
L = 0.656 m
What L is needed if temp changes, so
that the velocity of sound = 350 m/s?
• Now L = 0.669 m
The fifth harmonic of standing
waves in a pipe closed at one end is
512 Hz. How long is the pipe? Use
v = 343 m/s.
• f5 = 5v/4L,
• L = 0.84 m
A piano string is 1.10 m long. If it supports
a fundamental frequency with a velocity of
288 m/s, what would be the wavelength?
What is the fundamental frequency? The
second, third and fourth harmonics?
• Wavelength is 2.2 m,
• f1= 131 Hz, f2 = 262, f3 = 393, f4 =
524 Hz
Draw the standing wave patterns.
Label the nodes and antinodes.
For a string with both ends fixed
Organ Pipes Open at both ends
Organ Pipe with one end closed
A train is traveling at 44.7 m/s when
the engineer sounds a warning horn at
415 Hz. The speed of sound is 343
m/s. What are the frequencies and
wavelengths heard by a person
standing at the crossing as the train
approaches and leaves?
Approaches: f = 477 Hz λ =0.719m
leaves, f = 367 λ = 0.935
If a police car emits sounds its
horn (250 Hz) while stationary,
what frequency would be heard
by an observer approaching it at
27 m/s (60 mph)?
Use v = 340 m/s.
270 Hz