UniversityPhysicsVolume1-Ch16.  Florida State College at Jacksonville PHY 2048C

OpenStax University Physics Volume I
Unit 2: Waves and Acoustics
Chapter 16: Waves
University Physics Volume I
Unit 2: Waves and Acoustics
Chapter 16: Waves
Conceptual Questions
1. Give one example of a transverse wave and one example of a longitudinal wave, being careful
to note the relative directions of the disturbance and wave propagation in each.
Solution
A wave on a guitar string is an example of a transverse wave. The disturbance of the string
moves perpendicular to the propagation of the wave. The sound produced by the string is a
longitudinal wave where the disturbance of the air moves parallel to the propagation of the wave.
2. A sinusoidal transverse wave has a wavelength of 2.80 m. It takes 0.10 s for a portion of the
string at a position x to move from a maximum position of y=0.03 m to the equilibrium
position y=0. What are the period, frequency, and wave speed of the wave?
Solution
One-quarter of the period is equal to 0.10 s, so the period is 0.40 s. The frequency is
1 1
2.5 Hz.
0.40 s
f
T
= = =
The wave speed is
2.80 m
7.00 m/s.
0.40 s
v
T
= = =
3. What is the difference between propagation speed and the frequency of a mechanical wave?
Does one or both affect wavelength? If so, how?
Solution
Propagation speed is the speed of the wave propagating through the medium. If the wave speed
is constant, the speed can be found by
v f .
T
= =
The frequency is the number of wave that
pass a point per unit time. The wavelength is directly proportional to the wave speed and
inversely proportional to the frequency.
4. Consider a stretched spring, such as a slinky. The stretched spring can support longitudinal
waves and transverse waves. How can you produce transverse waves on the spring? How can
you produce longitudinal waves on the spring?
Solution
To produce transverse waves on the spring, wiggle the end of the spring up and down. The
disturbance of the spring will move up and down, perpendicular to the motion of the wave. To
produce longitudinal waves, pull a few coils together, compressing the coils, and then release.
The disturbance of the spring will move back and forth, parallel to the motion of the wave.
5. Consider a wave produced on a stretched spring by holding one end and shaking it up and
down. Does the wavelength depend on the distance you move your hand up and down?
Solution
No, the distance you move your hand up and down will determine the amplitude of the wave.
The wavelength will depend on the frequency you move your hand up and down, and the speed
of the wave through the spring.
6. A sinusoidal, transverse wave is produced on a stretched spring, having a period T. Each
section of the spring moves perpendicular to the direction of propagation of the wave, in simple
harmonic motion with an amplitude A. Does each section oscillate with the same period as the
wave or a different period? If the amplitude of the transverse wave were doubled but the period
stays the same, would your answer be the same?
Soluti