Sound is produced by vibrating objects like guitar strings and transmitted as longitudinal pressure waves through a medium like air. The speed of sound depends on properties of the medium and can be calculated using bulk modulus and density. Sound intensity is measured in decibels relative to the quietest sound detectable by humans. Guitar strings have unique fundamental frequencies that determine the pitch of the notes produced.

2.  Sound waves are produced by vibrating objects, such as a
guitar string.
 Sound is a longitudinal wave. As a guitar string vibrates, it
causes surrounding air molecules to oscillate in a direction
which is either parallel or anti-parallel to the propagation of
the wave.
 The displacement of the air particles results in a pressure
wave composed of compressions (high pressure) and
rarefractions (low pressure).
 A sound wave is the alternating pattern of compressions and
rarefractions.

3.  The speed of sound depends on the property of the
medium though which it is propagating.
 Calculating speed requires the introductions of bulk
modules (B) which represents the ‘stiffness’ of air.
B= -V ∆p
∆V
 Using the bulk module and the density of the medium
(air), velocity of sound can be determined.
v=

4. Question 1
Calculate the speed of sound in air. (B= 1.01x105 Pa, ρ=
1.2 kg/m2)

5. Answer: 290 m/s (NOTE: this answer is obtained from
using the information provided in the textbook. The
experimentally determined velocity of sound in air is 343
m/s)
Using the formula on the previous, divide B by the density
and take the square root.

6.  The decibel (dB) is a commonly used measurement of sound
intensity or power.
 Decibels are referenced to the quietest sound that a human
ear can detect (Io= 10-12 W/m2).
 The following equation is used to determine any other sound
intensity level
β(I)=0 dB+10 log(I/Io)

7. Question 2
Calculate the sound intensity level of a note plucked by an
unknown string that has an intensity of 7.5x10-6 W/m2..

8. Answer: 68.75 dB
Using the equation on the previous slide and I0= 10-12
dB= 10 log(7.5x10-6/10-12)

9.  The strings of a guitar have their own unique frequencies.
String Note Frequency
1 E (high) 329.6
2 B 246.9
3 G 196.0
4 D 146.8
5 A 110.0
6 E (low) 82.4

10. The frequency of the oscillation of air particles is the same as
the frequency of the vibration in the guitar string.
The following slide is a video of me plucking the low E string
on my guitar. The sound wave of the note has the same
frequency as the wave of the string which can be seen.

11. Question 3
Calculate the fundamental frequency of the same
unknown string given the length of the string to equal 80
cm and the velocity to equal 400 m/s. (Hint: λ= 2L when
determining the fundamental frequency)

12. Answer: 250 Hz
f= v/λ
λ= (80 cm×2)/ 100 m= 1.6 m
f= (400 m/s)/(1.6 m)= 250 Hz which approximately
corresponds to a B-string.

13.  The phase relationship between the pressure variations and
the displacement is as follows
∆p=Bksmsin(kx-ωt+ϕ)
B= Bulk modulus
k= 2π/λ
ω= 2π/T
sm= displacement
 To find the amplitude of the pressure variations as the
coefficient of the sine factor use the following equation
∆pm= Bksm

14. Question 4
Calculate the displacement amplitude of the sound waves
of the B-string with a pressure amplitude of 5.0×10-2 Pa.
(Use 343 m/s for velocity of sound in air)

15. Answer: 1.08×10-7 m
Known values: 343 m/s, 250 Hz, 1.01×105 Pa, 5.0×10-2 Pa
Sm=∆p/Bk
Sm= (5.0×10-2 Pa)/((1.01×105 Pa)(2π(250 Hz)/(343 m/s))

16. Works Cited
Hawkes Et Al. Physics for Scientists and Engineers: An
Interactive Approach. Vol. 1. Vancouver: U of British
Columbia, n.d. Print.
"Standard Guitar Tuning – EADGBE | Pro Guitar Tuner." Pro
Guitar Tuner. N.p., n.d. Web. 20 Feb. 2015.