This document compares the velocity of waves on strings or springs to the velocity of sound waves in gases or liquids. It explains that the velocity of waves on strings/springs is directly proportional to the tension, while the velocity of sound waves is directly proportional to pressure over fractional change in volume. It also discusses why velocity is inversely proportional to density for strings/springs, but not for sound waves, where a denser medium allows for faster particle movement. Sample problems are included about how changing pressure and density would affect wave velocities.

1. Christine Vu
49771141
L2H
Velocity of Waves on String or Springs
vs.
Velocity of Sound Waves in a Gas or Liquid
______Waves on String or Springs Sound Waves in a Gas/Liquid_____
v = T v = p / ( V/V)
--------- ------------------
density of string density of gas/liquid
T = how “stiff” the string/spring is p/ ( V/V) = how easy a unit volume of
fluid can be changed when changing
the pressure working on it
To aid in visualization of the problem To aid in visualization of the problem
involving velocity of waves on string/springs: involving velocity of sound waves:
Why is ‘v’ proportional to T? Why is ‘v’ proportional to p/ ( V/V) = B?
The value of ‘T’ helps us envision how The value of ‘B’ can be interpreted as
much force each particle in the spring/string “the fraction that the volume changes
is experiencing. The larger the tension, the when the pressure exerted on the medium
larger the velocity. changes” (Physics Textbook).
The force tension encourages the particles to The ratio of change in pressure to
line up in the direction of the force. A dis- change in fraction of volume is a relation-
placement of the particles (ie. A wave) under ship defined by the properties of the part-
the influence of the tension force will want icles of the medium. An increase in pressure
return to the equilibrium position as soon as that is initially being exerted on the part-
possible after the disruption because of the icles encourages the particles to move in a
encouraged alignment from the tension force. specific direction, much like the tension
force in a string or spring.
A decrease in volume implies an increase
in pressure, resulting in the same effect on
the particles described above.
An increase in pressure or decrease in
volume results in a larger velocity of the
sound wave because of the encouraged
alignment of the medium’s particles
Why is ‘v’ inversely proportional to the Why is ‘v’ inversely proportional to the
density of the string or spring? density of the medium?
A larger mass per volume means more part- Trick question! Velocity of sound waves
icles that the wave must travel through. Intui- are not inversely proportional to the density
tively, a larger amount of particles decreases of the medium. The denser the medium,
the momentum of the wave, resulting in a the larger the velocity. This is because the
lower velocity. presence of many particles allows for
more “bumping” of particles, which
results in a faster moving wave.

2. Christine Vu
49771141
L2H
Practice Problems
1) How would the velocity of the wave travelling a string change if the density of the
medium it was travelling through increased?
Answer: the velocity would decrease.
Why? The denominator of the wave-through-string velocity equation increases because of
the increase in pressure, which results in a smaller overall value of velocity.
2) How would the velocity of the sound wave change if the pressure of the system that
the sound wave was travelling through increased?
Answer: the velocity would increase.
Why? The numerator of the sound wave velocity equation increases because of the increase
in pressure, resulting in a larger overall value of velocity.
3) The bulk modulus decreased by a factor of 4. By what factor would the velocity of
the sound wave change?
Answer: the velocity would increase by a factor of 2.
Why? ‘B’ was multiplied by 4, but the square root in the equation squares the factor,
resulting in the sound wave velocity equation being multiplied by only 2 and not 4.

3. Christine Vu
49771141
L2H
Works Cited
Hawkes, R., et al. Physics for Scientists and Engineers: An Interactive Approach. Nelson.
The Engineering Toolbox. Bulk Modulus and Fluid Elasticity [online]. Available from
http://www.engineeringtoolbox.com/bulk-modulus-elasticity-d_585.html [accessed
21 February 2015].