The 42nd Period | STEM Education Hub

Sound waves are invisible, but the same math applies to a wave you can absolutely see and measure with your own hands: a spring. Today you'll build both wave types physically, then prove v = fλ actually works before ever applying it to something you can't watch happen.

🎯 Goals

Physically create transverse and longitudinal waves with a spring, and identify which one models sound.
Measure a wave's frequency and wavelength directly, and use v = fλ to calculate its speed.
Check a calculated wave speed against a directly-timed one.
Apply v = fλ to calculate the wavelength of real sound frequencies in air.

🧰 Materials

🌀A slinky or long spring

🪢A length of rope or thick cord (optional, for a second wave surface)

⏱️Stopwatch

📏Meter stick or tape measure

🔔Tuning forks or a printed frequency chart (256 Hz, 440 Hz, 512 Hz)

📓Physics notebook

DAY 1

Two Kinds of Waves

Section 1 of 4

Make Both Wave Types

With a partner holding the other end, shake your slinky side to side (or up and down).

Watch the wave pattern — the coils move perpendicular to the direction the wave travels down the spring. This is a transverse wave.

Now push and pull your end sharply along the spring's own length.

Watch the coils bunch up and spread apart as the disturbance travels down the spring. This is a longitudinal wave.

Sketch both wave types in your notebook, and label which one models sound.

Be specific about what's moving which direction relative to the wave's travel in each sketch.

⚠️ Sound is longitudinal — if your sketch shows sound as an up-and-down wiggle, go back and fix it before moving on.

📓 Physics Notebook

Describe, in your own words, what's different about how the coils move in the transverse wave versus the longitudinal wave.

DAY 2

Measure and Check

Section 2 of 4

Measure a Real Wave

Shake your spring or rope at a slow, steady rate and count oscillations over 10 seconds to find its frequency.

frequency = number of oscillations ÷ time. Keep your shaking rate as steady as you can.

With the wave running steadily, measure the distance from one crest to the next with a ruler — that's your wavelength.

You may need a partner to help freeze the pattern in place, or take a quick photo to measure from.

Calculate the wave's speed using v = fλ.

Record your frequency, wavelength, and calculated speed.

Section 3 of 4

Check Your Speed Directly

Send a single quick pulse down the spring and time how long it takes to travel a measured length.

speed = distance ÷ time. This gives you a second, independent measurement of the same wave speed.

Compare your two speed values.

They won't match perfectly — that's expected with hand-timed, hand-measured data. The question is whether they're in the same ballpark.

Trial	Frequency (Hz)	Wavelength (m)	v = fλ (m/s)	Direct-timed v (m/s)

📓 Physics Notebook

How close were your two speed measurements? What's the biggest source of error in a hand-timed, hand-measured setup like this one?

Section 4 of 4

Apply It to Sound

Using v = 343 m/s for sound in air, calculate the wavelength for each frequency in the table below.

These are the same equation, same algebra — just a different (invisible) wave.

Sound source	Frequency (Hz)	Wavelength (m)

Question 1

Explain why you can measure a spring wave's wavelength directly with a ruler, but you can't do the same thing for a sound wave in air.

Question 2

If you doubled your shaking frequency on the spring, what would happen to the wavelength? Explain using v = fλ.

Question 3

A higher-pitched tuning fork has a shorter wavelength than a lower-pitched one, assuming both are in air. Explain why, using the wave equation.

📤 Turn In

Sketches of both wave types, correctly labeled
Completed spring-wave measurement table with both speed calculations
Completed sound-wavelength table
Written answers to the three Conclusion questions

← Back to Activity 3-1-1 Overview Review the Deep Dive →Next up: Lesson 3-1-2, Pitch & Loudness.