Waves transfer energy from one place to another without transferring matter overall. This cheat sheet helps students connect wave diagrams, measurements, and equations used in physics problems. It focuses on mechanical waves, sound waves, and the relationships among speed, frequency, wavelength, period, amplitude, and energy.
These ideas are important for understanding sound, music, earthquakes, light behavior, and many everyday technologies.
The main wave equation is , which connects wave speed, frequency, and wavelength. Period and frequency are related by , so a wave that repeats more often has a shorter period. Sound is a longitudinal mechanical wave, and its loudness is often measured using intensity and decibels.
Interference, resonance, standing waves, and the Doppler effect explain many real sound patterns and wave behaviors.
Key Facts
- Wave speed is found with , where is speed, is frequency, and is wavelength.
- Frequency and period are reciprocals, so and .
- For a wave on a string, speed depends on tension and linear mass density according to .
- Sound intensity is power per area, given by , and is measured in .
- Sound level in decibels is calculated with , where .
- For an open-open pipe or a string fixed at both ends, standing wave wavelengths follow for .
- For an open-closed pipe, standing wave wavelengths follow for odd values .
- The Doppler effect changes observed frequency because of relative motion, with higher frequency when the source and observer move toward each other.
Vocabulary
- Wavelength
- Wavelength is the distance between matching points on neighboring waves, such as crest to crest or compression to compression.
- Frequency
- Frequency is the number of complete wave cycles that pass a point each second, measured in hertz.
- Period
- Period is the time for one complete wave cycle, and it is related to frequency by .
- Amplitude
- Amplitude is the maximum displacement from the rest position and is related to the energy carried by a wave.
- Longitudinal Wave
- A longitudinal wave has particles that vibrate parallel to the direction the wave travels, as in sound waves in air.
- Resonance
- Resonance occurs when an object vibrates with a large amplitude because it is driven near one of its natural frequencies.
Common Mistakes to Avoid
- Confusing frequency with period is wrong because counts cycles per second while measures seconds per cycle, and they are related by .
- Using crest-to-trough distance as wavelength is wrong because is measured from crest to crest, trough to trough, or compression to compression.
- Assuming louder sound always travels faster is wrong because sound speed depends mainly on the medium and temperature, not on amplitude.
- Forgetting that sound needs a medium is wrong because sound is a mechanical wave and cannot travel through a vacuum.
- Using all harmonics for an open-closed pipe is wrong because open-closed pipes only support odd harmonics, so .
Practice Questions
- 1 A water wave has a frequency of and a wavelength of . What is its speed?
- 2 A sound wave travels at and has a frequency of . What is its wavelength?
- 3 A student measures for one complete vibration of a tuning fork. What are the period and frequency?
- 4 Explain why the pitch of a siren sounds higher as an ambulance approaches and lower after it passes.
Understanding Waves & Sound
A wave diagram can be misleading if students treat it as the path followed by a particle. In a transverse wave on a rope, each small piece of rope moves up and down while the pattern travels along the rope. In a longitudinal sound wave, air particles move back and forth in the same direction as the sound travels.
The crowded regions are compressions and the spread out regions are rarefactions. A microphone detects these pressure changes and turns them into an electrical signal. Human ears do something similar with the eardrum and inner ear.
Wave speed is usually set by the medium, not by how hard the source is shaken. A tighter guitar string carries disturbances faster because tension pulls each section back more strongly. A heavier string tends to respond more slowly.
In air, sound travels faster in warmer conditions because molecules move faster and pass pressure changes along more quickly. When a source changes its frequency in one unchanged medium, the speed stays nearly constant.
The wavelength must then change to fit the new frequency. This is why a high musical note has a shorter wavelength than a low note in the same room.
Amplitude needs careful interpretation. A greater amplitude on a rope means a larger displacement from the rest position. For sound, it means larger pressure variations in the air.
Larger variations usually carry more energy and are heard as louder sound. Loudness is not perfectly physical because human ears respond differently to different frequencies. Decibels are especially important because the scale is logarithmic.
An increase of ten decibels means the sound intensity becomes ten times greater. It does not simply mean a small extra amount of sound. This helps explain why headphones, concerts, traffic, and machinery can reach harmful levels sooner than people expect.
Resonance occurs when repeated pushes arrive at the right timing to build a larger vibration. A playground swing rises higher when each push matches its natural rhythm. Air columns in wind instruments behave in the same way.
Reflections from the ends create standing waves with fixed points called nodes and locations of greatest motion called antinodes. The allowed patterns depend on whether an end is open or closed, which determines the notes an instrument can produce. The Doppler effect is different because it comes from motion between source and listener.
A passing ambulance sounds higher while approaching and lower after passing. The source does not need to change its actual frequency. Students should first identify the medium, boundary conditions, and relative motion before choosing a wave model or calculation.