The Wave Equation - Free Printable

You're given the wave equation:

> Wave speed (velocity) = Frequency × Wavelength
> or in symbols:
> v = f × λ

Where:
- v = wave speed in meters per second (m/s)
- f = frequency in Hertz (Hz)
- λ (lambda) = wavelength in meters (m)

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## ✔ Step 1: Fill in the Table

We’ll use v = f × λ to fill in missing values.

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Row 1: Speed = ?, Frequency = 20 Hz, Wavelength = 2.5 m

→ v = 20 × 2.5 = 50 m/s

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Row 2: Speed = 330 m/s, Frequency = 150 Hz, Wavelength = 0.75 m

→ Check: 150 × 0.75 = 112.5 → ✘ Doesn’t match 330
Wait — this row has Speed = 330, Frequency = 150, so find Wavelength:
→ λ = v / f = 330 / 150 = 2.2 m

But the table says wavelength is 0.75 — that’s inconsistent. Let’s assume the speed and frequency are correct, and we need to calculate wavelength.

✔ So corrected: Wavelength = 330 / 150 = 2.2 m

*(Note: There might be a typo in the original table — perhaps frequency or wavelength was meant to be different. But since you’re told to “use a calculator to fill in”, we’ll compute based on two knowns.)*

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Row 3: Speed = 1500 m/s, Frequency = 600 Hz, Wavelength = ?

→ λ = v / f = 1500 / 600 = 2.5 m

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Row 4: Speed = 0.5 m/s, Wavelength = 5 m, Frequency = ?

→ f = v / λ = 0.5 / 5 = 0.1 Hz

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Row 5: Speed = ?, Frequency = 0.05 Hz, Wavelength = 1573 m

→ v = 0.05 × 1573 = 78.65 m/s

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Row 6: Speed = 0.34 m/s, Wavelength = 10700 m, Frequency = ?

→ f = 0.34 / 10700 ≈ 0.0000317757 Hz → Round to 3.18 × 10⁻⁵ Hz

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Row 7: Speed = 300,000,000 m/s, Wavelength = 2 m, Frequency = ?

→ f = 300,000,000 / 2 = 150,000,000 Hz = 150 MHz

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Row 8: Speed = 0.00006 m/s, Frequency = 0.098 Hz, Wavelength = ?

→ λ = v / f = 0.00006 / 0.098 ≈ 0.00061224 m → or 6.12 × 10⁻⁴ m

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## 📊 Completed Table:

| Speed m/s | Frequency Hz | Wavelength m |
|-----------------|------------------|----------------|
| 50 | 20 | 2.5 |
| 330 | 150 | 2.2 |
| 1500 | 600 | 2.5 |
| 0.5 | 0.1 | 5 |
| 78.65 | 0.05 | 1573 |
| 0.34 | 3.18×10⁻⁵ | 10700 |
| 300000000 | 150000000 | 2 |
| 0.00006 | 0.098 | 0.000612 |

*(Note: I’ve corrected inconsistencies assuming two values are given and one is calculated.)*

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## ✔ Q1: Sound wave: λ = 2m, f = 170 Hz → Find velocity

v = f × λ = 170 × 2 = 340 m/s

✔ Answer: 340 m/s

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## ✔ Q2: Same wave enters water → speed = 1500 m/s, frequency unchanged → find new wavelength

Frequency remains 170 Hz (same as before).

Use: λ = v / f = 1500 / 170 ≈ 8.8235 m

✔ Answer: ≈ 8.82 m

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## ✔ Q3: Radio wave: v = 3×10⁸ m/s, f = 252 kHz → find wavelength

First, convert kHz to Hz:
252 kHz = 252,000 Hz = 2.52 × 10⁵ Hz

Now: λ = v / f = (3 × 10⁸) / (2.52 × 10⁵) = 1190.476... m

✔ Answer: ≈ 1190 m (or 1.19 km)

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## ✔ Q4: Another radio wave, same speed (3×10⁸ m/s), λ = 0.2 m → find frequency

f = v / λ = (3 × 10⁸) / 0.2 = 1.5 × 10⁹ Hz = 1500 MHz = 1.5 GHz

✔ Answer: 1.5 × 10⁹ Hz or 1.5 GHz

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## 🧠 Summary of Answers:

Table Filled (as above)

Q1: 340 m/s

Q2: ≈ 8.82 m

Q3: ≈ 1190 m

Q4: 1.5 × 10⁹ Hz (or 1.5 GHz)

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Let me know if you want the triangle diagram explained too! (It’s often called the “wave triangle” — cover the variable you want to find, and the other two show the operation: e.g., cover v → f × λ; cover f → v ÷ λ, etc.)

Hope this helps! 🎯