Chapter
10 & 11
Elasticity,
Oscillations,
Waves,
and Sound
Mechanical
Waves
A
progressive or traveling wave is a selfsustaining disturbance of
a medium that propagates from one region to another, carrying
energy and momentum.
Longitudinal
Wave – the sustaining medium is displaced parallel to the direction
of propagation.
Transverse
Wave – the sustaining medium is displaced perpendicular to the direction
of propagation.
Period – the time it takes for a wave to go through one complete
oscillation.
Frequency – the number of complete oscillations the wave makes in
a second.
Wavelength – the spatial distance over which the wave makes one complete
oscillation.
Speed of any progressive periodic wave:
(16)
Problem
16
Sound
waves travel in air with a speed of 343 m/s. The lowest
frequency sound we can hear is 20.0 Hz; the highest frequency
is 20.0 kHz. Find the wavelength of sound for frequencies
of 20.0 Hz and 20.0 kHz.
Solution:
Solve
equation (16) for the wavelength:
Transverse
Waves: Strings
Speed
of a transverse wave in a string:
(17)
where is
the tension in the string and m/L is the mass per unit
length.
Example
17
A
5.0 m length of rope, with a mass of 0.52 kg, is pulled
taut with a tension of 46 N. Find the speed of waves on
the rope.
Solution:
Use
equation (17) to find the speed of the wave:
Example
18
A
12 m rope is pulled tight with a tension of 92 N. When
one end of the rope is given a "thunk" it takes 0.45 s
for the disturbance to propagate to the other end. What
is the mass of the rope?
Solution:
Calculate
the speed of the wave:
Use
equation (17) to solve for the mass:
Sound Part 2
