Physics Worksheet

🎸 Standing Waves

Chapter: Waves · Level ★★☆ · Time: 30 min

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NameClassDate

After this worksheet you can

Understand: How Standing Waves FormUnderstand: Nodes and AntinodesUnderstand: Standing Waves on a String (Fixed at Both Ends)Understand: Fundamental Frequency and Harmonics

📚 Quick Recap

A standing wave forms when two identical waves traveling in opposite directions interfere, creating a pattern that appears to oscillate in place rather than travel — the physics behind every musical instrument.

🧠 Section A · Concept Check ● BEGINNER 4 × 1 = 4

1A string of length 1.5m is fixed at both ends. Find the fundamental wavelength.

2A string's fundamental frequency is 220Hz. Find its 4th harmonic frequency.

3A string of length 2m has a standing wave with n=2. Find its wavelength.

4Why do only specific wavelengths 'fit' on a string fixed at both ends?

🧮 Section B · Problem Solving ● INTERMEDIATE 4 × 3 = 12

5A guitar string produces a fundamental frequency of 330Hz. Find its 5th harmonic.

6Why do musical instruments produce specific, distinguishable pitches rather than random noise?

7How many nodes does the fundamental (n=1) standing wave have on a string fixed at both ends (not counting the two fixed ends, which are also nodes)?

8How many antinodes does the fundamental (n=1) standing wave have?

🚀 Section C · Challenge ● CHALLENGE 2 × 2 = 4

9A string has fundamental frequency 150Hz. Is 450Hz one of its harmonics? If so, which one?

10Why is understanding standing waves essential for designing musical instruments?

💭 Reflection — the most useful thing I learned:

A ___/4 B ___/12 C ___/4 Total ___/20 Teacher's Signature Parent's Signature

✂ answer key — fold or cut before handing out

1 = 3m 2 = 880Hz 3 = lambda_2=2*2/2=2m 4 = Both ends must be nodes (fixed, zero displacement), which only occurs for wavelengths that divide evenly into twice the string length | 5 = 1650Hz 6 = Standing waves only form at specific resonant frequencies (harmonics) determined by the instrument's length and boundary conditions 7 = 0 additional nodes between the ends (just the two endpoints) 8 = 1 antinode (in the middle) | 9 = Yes, the 3rd harmonic (450=3*150) 10 = It determines exactly what pitches (frequencies) an instrument can naturally produce based on its physical dimensions