24.1 Section Review
1. A turn of a wheel is an example of one cycle.
2. Examples of oscillating systems at an amusement park: a Ferris wheel, a pirate ship pendulum ride, any ride that goes
around in circles, any ride that swings back and forth, the path of a roller coaster is a kind of oscillator because it repeats
its path over and over (in effect it travels in a circle even though it may go up and down, upside down, or around in a
corkscrew).
3. Frequency (cycles per second) equals the inverse of period (the number of seconds per cycle).
4. The period is 5 seconds: (10 seconds ÷ 2 cycles = 5 seconds/cycle). The frequency is 0.2 Hz: (1 cycle/5 seconds =
0.2cycle/s).
5. A graph of harmonic motion will have a repeating pattern. A linear graph does not have a repeating pattern.
6. The amplitude of this pendulum is 5 centimeters.
7. The period of the pendulum is 2 seconds.
8. The resistance of a spring to being extended or compressed acts as a restoring force so, yes, a spring is a simple
oscillator. When the spring is compressed, it pushes back on the mass. When the spring is extended, it pulls on the mass.
The push-pull of the spring is a restoring force and the mass supplies the inertia. An example of a mass on a spring is a
car (mass) and its shock absorbers (springs). Wheels on springs can oscillate up and down over bumps without the whole
car having to move up and down too (or as much). Along with springs, shock absorbers also have high friction dampers
that quickly slow any oscillation down. A car that keeps bouncing after going over a bump has shock absorbers with
dampers that are worn out and not providing enough friction.
9. The pendulum with the longer string will have the longer period.
10. Mass does not affect the period of a pendulum because of Newton’s second law of motion (a = F/m). An increase in
mass will be balanced by a greater force needed to accelerate the pendulum (because one of the forces acting on it is
gravity and Earth will still accelerate all masses at -9.8 m/s/s), however the inertia will increase.
11. The answer is: (a) a periodic force is applied at the natural frequency.
24.2 Section Review
1. Answers:
a. The amplitude is 2 centimeters (half the distance from the crest to the trough).
b. The wavelength is 10 centimeters.
2. The wavelength is 2.5 meters.
3. v = frequency × wavelength: (10 Hz × 0.4 meter = 4 m/s)
4. Use the wave speed formula: v = frequency × wavelength: (20 m/s = 1/T × 1 meter). Then, find the period: (T = 1
meter ÷ 20 m/s = 0.05 s).
5. Answers:
a. Absorption
b. Refraction
c. Reflection
d. Absorption
e. Refraction
f. Diffraction
6. During absorption of a wave, the amplitude (and the energy) decrease.
7. Transverse waves, such as water waves (and light waves), have an oscillation that is perpendicular to the direction of
motion. Longitudinal waves, such as sound waves, have an oscillation that is in the same direction as the motion.
8. This is an example of constructive interference.
9. The volume of a sound wave is directly related to its amplitude.
24.3 Section Review
2. The two frequency spectrums would be different for two different people saying the word “dog.” This is because each
person has a unique mix of frequencies that characterizes their voice (remember, every wave has its own “signature”).
3. The two variables that affect how loudly you hear a sound are its intensity and frequency. The intensity of a sound is
measure in decibels and is related to its amplitude (for every 20-increment increase in decibel level, the amplitude
increases 10-fold).
6. This object would be subsonic and traveling at 160 km/h.
7. Sound travels faster through water because water molecules are closer together so there is a greater restoring force
between them than between air molecules (which are very far apart). Sound needs atoms and molecules to vibrate and
to push against each other in order to travel through space.
9. No, you would not hear beats. Beats occur when two frequencies of sound are not exactly equal in value so that the
loudness of the total sound seems to oscillate or beat.
11. On average, people gradually lose high-frequency hearing with age. So, if you were talking to an elderly person, it
would be better to use a deeper, lower-frequency, voice.
12. The paramedic is traveling with the sound and therefore does not experience the Doppler Effect. In order to
experience the Doppler Effect you need have the sound moving away from you or toward you (or you moving
away/toward it will some appreciable speed).
13. The ambulance is traveling away from me because the pitch (frequency) is getting lower. The sound waves are not
compressed in this case. If the ambulance was traveling toward me, the sound waves would be compressed and the
sound would be higher pitched (higher frequency).
14. When two sound waves are slightly out of phase, you will hear beats (alternating louder and softer sounds) as they
interfere with each other constructively and destructively.