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Wave Speed, Frequency and Wavelength worksheet

Grades 8–9 · CCSS HSA.CED.A.4, 8.EE.A.4

Solve each problem and show your work. Round answers to 2 decimal places where needed.

1.
Problem 1.
- Solve for: Frequency (f)
- Wave speed: Sound in air at 20 °C: ≈343 m/s
- Wavelength (λ): 1 m
- Show frequency in: Megahertz (MHz)
Find: Frequency
Answer
2.
Problem 2.
- Solve for: Wave speed (v)
- Frequency (f): 520 Hz
- Wavelength (λ): 0.6 m
- Show wave speed in: Miles per hour (mph)
Find: Wave speed
Answer
3.
Problem 3.
- Solve for: Wavelength (λ)
- Wave speed: Light in a vacuum: 299,792,458 m/s (exact)
- Frequency (f): 300 Hz
- Show wavelength in: Kilometers (km)
Find: Wavelength
Answer
4.
Problem 4.
- Solve for: Frequency (f)
- Wave speed: Enter a wave speed
- Wave speed (v): 1,500 m/s
- Wavelength (λ): 0.75 m
- Show frequency in: Kilohertz (kHz)
Find: Frequency
Answer
5.
Problem 5.
- Solve for: Wave speed (v)
- Frequency (f): 400 Hz
- Wavelength (λ): 0.7 m
- Show wave speed in: Kilometers per hour (km/h)
Find: Wave speed
Answer
6.
Problem 6.
- Solve for: Wavelength (λ)
- Wave speed: Sound in air at 20 °C: ≈343 m/s
- Frequency (f): 500 Hz
- Show wavelength in: Nanometers (nm)
Find: Wavelength
Answer
7.
Problem 7.
- Solve for: Wave speed (v)
- Frequency (f): 500 Hz
- Wavelength (λ): 1.1 m
- Show wave speed in: Miles per hour (mph)
Find: Wave speed
Answer
8.
Problem 8.
- Solve for: Wavelength (λ)
- Wave speed: Sound in air at 20 °C: ≈343 m/s
- Frequency (f): 450 Hz
- Show wavelength in: Feet (ft)
Find: Wavelength
Answer
9.
Problem 9.
- Solve for: Wave speed (v)
- Frequency (f): 500 Hz
- Wavelength (λ): 0.56 m
- Show wave speed in: Meters per second (m/s)
Find: Wave speed
Answer
10.
Problem 10.
- Solve for: Wavelength (λ)
- Wave speed: Light in a vacuum: 299,792,458 m/s (exact)
- Frequency (f): 450 Hz
- Show wavelength in: Centimeters (cm)
Find: Wavelength
Answer

Answer key: Wave Speed, Frequency and Wavelength worksheet

1. Frequency: 3.43e-4 MHz
1. Use the speed of sound in dry air at 20 °C (approximate)
  $v$ $= 343 m/s$
2. Find the frequency: divide the speed by the wavelength, because speed = frequency × wavelength
  $\frac{343}{1}$ $= 343 Hz$
3. Find the period, the time one full cycle takes: 1 ÷ the frequency
  $\frac{1}{343}$ $= 0.0029154519 s$
4. Change the answer to MHz, the unit you picked: divide by 1,000,000
  $\frac{343}{1,000,000}$ $= 0.000343 MHz$
2. Wave speed: 697.92 mph
1. Find the speed: multiply the frequency by the wavelength, since that's how far the wave goes each second
  $520 \times 0.6$ $= 312 m/s$
2. Find the period, the time one full cycle takes: 1 ÷ the frequency
  $\frac{1}{520}$ $= 0.0019230769 s$
3. Change the answer to mph, the unit you picked: divide by 0.44704
  $\frac{312}{0.44704}$ $= 697.924123 mph$
3. Wavelength: 999.31 km
1. Use the speed of light in a vacuum (exact)
  $v$ $= 299,792,458 m/s$
2. Find the wavelength: divide the speed by the frequency, because speed = frequency × wavelength
  $\frac{299,792,458}{300}$ $= 999,308.193333 m$
3. Find the period, the time one full cycle takes: 1 ÷ the frequency
  $\frac{1}{300}$ $= 0.0033333333 s$
4. Change the answer to km, the unit you picked: divide by 1,000
  $\frac{999,308.193333}{1,000}$ $= 999.308193 km$
4. Frequency: 2 kHz
1. Find the frequency: divide the speed by the wavelength, because speed = frequency × wavelength
  $\frac{1,500}{0.75}$ $= 2,000 Hz$
2. Find the period, the time one full cycle takes: 1 ÷ the frequency
  $\frac{1}{2,000}$ $= 0.0005 s$
3. Change the answer to kHz, the unit you picked: divide by 1,000
  $\frac{2,000}{1,000}$ $= 2 kHz$
5. Wave speed: 1,008 km/h
1. Find the speed: multiply the frequency by the wavelength, since that's how far the wave goes each second
  $400 \times 0.7$ $= 280 m/s$
2. Find the period, the time one full cycle takes: 1 ÷ the frequency
  $\frac{1}{400}$ $= 0.0025 s$
3. Change the answer to km/h, the unit you picked: divide by 0.277777777778
  $\frac{280}{0.277777777778}$ $= 1,008 km/h$
6. Wavelength: 686,000,000 nm
1. Use the speed of sound in dry air at 20 °C (approximate)
  $v$ $= 343 m/s$
2. Find the wavelength: divide the speed by the frequency, because speed = frequency × wavelength
  $\frac{343}{500}$ $= 0.686 m$
3. Find the period, the time one full cycle takes: 1 ÷ the frequency
  $\frac{1}{500}$ $= 0.002 s$
4. Change the answer to nm, the unit you picked: divide by 0.000000001
  $\frac{0.686}{0.000000001}$ $= 686,000,000 nm$
7. Wave speed: 1,230.31 mph
1. Find the speed: multiply the frequency by the wavelength, since that's how far the wave goes each second
  $500 \times 1.1$ $= 550 m/s$
2. Find the period, the time one full cycle takes: 1 ÷ the frequency
  $\frac{1}{500}$ $= 0.002 s$
3. Change the answer to mph, the unit you picked: divide by 0.44704
  $\frac{550}{0.44704}$ $= 1,230.314961 mph$
8. Wavelength: 2.5 ft
1. Use the speed of sound in dry air at 20 °C (approximate)
  $v$ $= 343 m/s$
2. Find the wavelength: divide the speed by the frequency, because speed = frequency × wavelength
  $\frac{343}{450}$ $= 0.762222 m$
3. Find the period, the time one full cycle takes: 1 ÷ the frequency
  $\frac{1}{450}$ $= 0.0022222222 s$
4. Change the answer to ft, the unit you picked: divide by 0.3048
  $\frac{0.762222}{0.3048}$ $= 2.500729 ft$
9. Wave speed: 280 m/s
1. Find the speed: multiply the frequency by the wavelength, since that's how far the wave goes each second
  $500 \times 0.56$ $= 280 m/s$
2. Find the period, the time one full cycle takes: 1 ÷ the frequency
  $\frac{1}{500}$ $= 0.002 s$
10. Wavelength: 66,620,546.22 cm
1. Use the speed of light in a vacuum (exact)
  $v$ $= 299,792,458 m/s$
2. Find the wavelength: divide the speed by the frequency, because speed = frequency × wavelength
  $\frac{299,792,458}{450}$ $= 666,205.462222 m$
3. Find the period, the time one full cycle takes: 1 ÷ the frequency
  $\frac{1}{450}$ $= 0.0022222222 s$
4. Change the answer to cm, the unit you picked: divide by 0.01
  $\frac{666,205.462222}{0.01}$ $= 66,620,546.222222 cm$