Waves & Sound Cheat Sheet

A printable reference covering wave speed, frequency, wavelength, period, amplitude, sound intensity, decibels, resonance, and Doppler effect for grades 9-10.

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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 $v=f\lambda$ , which connects wave speed, frequency, and wavelength. Period and frequency are related by $T=\frac{1}{f}$ , 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 $v=f\lambda$ , where $v$ is speed, $f$ is frequency, and $\lambda$ is wavelength.
Frequency and period are reciprocals, so $f=\frac{1}{T}$ and $T=\frac{1}{f}$ .
For a wave on a string, speed depends on tension and linear mass density according to $v=\sqrt{\frac{F_T}{\mu}}$ .
Sound intensity is power per area, given by $I=\frac{P}{A}$ , and is measured in $\text{W/m}^2$ .
Sound level in decibels is calculated with $\beta=10\log_{10}\left(\frac{I}{I_0}\right)$ , where $I_0=1.0\times10^{-12}\ \text{W/m}^2$ .
For an open-open pipe or a string fixed at both ends, standing wave wavelengths follow $\lambda_n=\frac{2L}{n}$ for $n=1,2,3,\ldots$ .
For an open-closed pipe, standing wave wavelengths follow $\lambda_n=\frac{4L}{n}$ for odd values $n=1,3,5,\ldots$ .
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 $T=\frac{1}{f}$ .
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 $f$ counts cycles per second while $T$ measures seconds per cycle, and they are related by $f=\frac{1}{T}$ .
Using crest-to-trough distance as wavelength is wrong because $\lambda$ 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 $n=1,3,5,\ldots$ .

Practice Questions

1 A water wave has a frequency of $4.0\ \text{Hz}$ and a wavelength of $2.5\ \text{m}$ . What is its speed?
2 A sound wave travels at $343\ \text{m/s}$ and has a frequency of $686\ \text{Hz}$ . What is its wavelength?
3 A student measures $0.20\ \text{s}$ 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.