Calculating Speed of Waves, frequency and Velocity worksheet ... - Free Printable

To solve the problems related to wavespeed, frequency, and wavelength, we use the wave equation:

\[
v = f \cdot \lambda
\]

Where:
- \( v \) is the wavespeed (in meters per second, m/s),
- \( f \) is the frequency (in hertz, Hz),
- \( \lambda \) is the wavelength (in meters, m).

We can rearrange this formula to solve for any one of the variables if the other two are known:
1. To find wavespeed (\( v \)): \( v = f \cdot \lambda \)
2. To find frequency (\( f \)): \( f = \frac{v}{\lambda} \)
3. To find wavelength (\( \lambda \)): \( \lambda = \frac{v}{f} \)

Let's solve each problem step by step.

---

Problem 1:

A wave has a frequency of 50 hertz and a wavelength of 10 meters. What is the wavespeed?

Given:
- \( f = 50 \, \text{Hz} \)
- \( \lambda = 10 \, \text{m} \)

Formula:
\[
v = f \cdot \lambda
\]

Solution:
\[
v = 50 \, \text{Hz} \cdot 10 \, \text{m} = 500 \, \text{m/s}
\]

Answer:
\[
\boxed{500 \, \text{m/s}}
\]

---

Problem 2:

A wave has a frequency of 5 Hz and a wavespeed of 25 m/s. What is the wavelength?

Given:
- \( f = 5 \, \text{Hz} \)
- \( v = 25 \, \text{m/s} \)

Formula:
\[
\lambda = \frac{v}{f}
\]

Solution:
\[
\lambda = \frac{25 \, \text{m/s}}{5 \, \text{Hz}} = 5 \, \text{m}
\]

Answer:
\[
\boxed{5 \, \text{m}}
\]

---

Problem 3:

A wave has a wavelength of 10 meters and a wavespeed of 340 m/s. What is the frequency of the wave?

Given:
- \( \lambda = 10 \, \text{m} \)
- \( v = 340 \, \text{m/s} \)

Formula:
\[
f = \frac{v}{\lambda}
\]

Solution:
\[
f = \frac{340 \, \text{m/s}}{10 \, \text{m}} = 34 \, \text{Hz}
\]

Answer:
\[
\boxed{34 \, \text{Hz}}
\]

---

Problem 4:

A wave with a frequency of 13 Hz and a wavelength of 4 meters. At what speed will the wave travel?

Given:
- \( f = 13 \, \text{Hz} \)
- \( \lambda = 4 \, \text{m} \)

Formula:
\[
v = f \cdot \lambda
\]

Solution:
\[
v = 13 \, \text{Hz} \cdot 4 \, \text{m} = 52 \, \text{m/s}
\]

Answer:
\[
\boxed{52 \, \text{m/s}}
\]

---

Problem 5:

A wave is moving at 65 m/s, and the wavelength is 1.5 meters. What is the frequency of the wave?

Given:
- \( v = 65 \, \text{m/s} \)
- \( \lambda = 1.5 \, \text{m} \)

Formula:
\[
f = \frac{v}{\lambda}
\]

Solution:
\[
f = \frac{65 \, \text{m/s}}{1.5 \, \text{m}} = 43.33 \, \text{Hz}
\]

Answer:
\[
\boxed{43.33 \, \text{Hz}}
\]

---

Problem 6:

A wave has a frequency of 46 Hz and a wavelength of 2.3 meters. What is the speed of the wave?

Given:
- \( f = 46 \, \text{Hz} \)
- \( \lambda = 2.3 \, \text{m} \)

Formula:
\[
v = f \cdot \lambda
\]

Solution:
\[
v = 46 \, \text{Hz} \cdot 2.3 \, \text{m} = 105.8 \, \text{m/s}
\]

Answer:
\[
\boxed{105.8 \, \text{m/s}}
\]

---

Problem 7:

A wave with the frequency of 500 Hz is traveling at a speed of 100 meters. What is the wavelength?

Given:
- \( f = 500 \, \text{Hz} \)
- \( v = 100 \, \text{m/s} \)

Formula:
\[
\lambda = \frac{v}{f}
\]

Solution:
\[
\lambda = \frac{100 \, \text{m/s}}{500 \, \text{Hz}} = 0.2 \, \text{m}
\]

Answer:
\[
\boxed{0.2 \, \text{m}}
\]

---

Problem 8:

A wave has a wavelength of 125 meters and is moving at a speed of 20 m/s. What is its frequency?

Given:
- \( \lambda = 125 \, \text{m} \)
- \( v = 20 \, \text{m/s} \)

Formula:
\[
f = \frac{v}{\lambda}
\]

Solution:
\[
f = \frac{20 \, \text{m/s}}{125 \, \text{m}} = 0.16 \, \text{Hz}
\]

Answer:
\[
\boxed{0.16 \, \text{Hz}}
\]

---

Problem 9:

A wave has a wavelength of 80 meters and has a frequency of 60 Hz. What is its velocity?

Given:
- \( \lambda = 80 \, \text{m} \)
- \( f = 60 \, \text{Hz} \)

Formula:
\[
v = f \cdot \lambda
\]

Solution:
\[
v = 60 \, \text{Hz} \cdot 80 \, \text{m} = 4800 \, \text{m/s}
\]

Answer:
\[
\boxed{4800 \, \text{m/s}}
\]

---

Problem 10:

A wave has a velocity of 45 m/s and a wavelength of 9 meters. What is the wave’s frequency?

Given:
- \( v = 45 \, \text{m/s} \)
- \( \lambda = 9 \, \text{m} \)

Formula:
\[
f = \frac{v}{\lambda}
\]

Solution:
\[
f = \frac{45 \, \text{m/s}}{9 \, \text{m}} = 5 \, \text{Hz}
\]

Answer:
\[
\boxed{5 \, \text{Hz}}
\]

---

Problem 11:

A wave is moving at 300 m/s and has a frequency of 25 Hz. What is the wavelength?

Given:
- \( v = 300 \, \text{m/s} \)
- \( f = 25 \, \text{Hz} \)

Formula:
\[
\lambda = \frac{v}{f}
\]

Solution:
\[
\lambda = \frac{300 \, \text{m/s}}{25 \, \text{Hz}} = 12 \, \text{m}
\]

Answer:
\[
\boxed{12 \, \text{m}}
\]

---

Problem 12:

A wave has a frequency of 53 Hz and a wavelength of 4 meters. What is its wavespeed?

Given:
- \( f = 53 \, \text{Hz} \)
- \( \lambda = 4 \, \text{m} \)

Formula:
\[
v = f \cdot \lambda
\]

Solution:
\[
v = 53 \, \text{Hz} \cdot 4 \, \text{m} = 212 \, \text{m/s}
\]

Answer:
\[
\boxed{212 \, \text{m/s}}
\]

---

Problem 13:

A wave has a velocity of 72 m/s and a frequency of 12 Hz. What is the wavelength?

Given:
- \( v = 72 \, \text{m/s} \)
- \( f = 12 \, \text{Hz} \)

Formula:
\[
\lambda = \frac{v}{f}
\]

Solution:
\[
\lambda = \frac{72 \, \text{m/s}}{12 \, \text{Hz}} = 6 \, \text{m}
\]

Answer:
\[
\boxed{6 \, \text{m}}
\]

---

Problem 14:

A wave has a wavelength of 87 meters and a frequency of 4 Hz. What is the wavespeed?

Given:
- \( \lambda = 87 \, \text{m} \)
- \( f = 4 \, \text{Hz} \)

Formula:
\[
v = f \cdot \lambda
\]

Solution:
\[
v = 4 \, \text{Hz} \cdot 87 \, \text{m} = 348 \, \text{m/s}
\]

Answer:
\[
\boxed{348 \, \text{m/s}}
\]

---

Final Answers:

1. \( \boxed{500 \, \text{m/s}} \)
2. \( \boxed{5 \, \text{m}} \)
3. \( \boxed{34 \, \text{Hz}} \)
4. \( \boxed{52 \, \text{m/s}} \)
5. \( \boxed{43.33 \, \text{Hz}} \)
6. \( \boxed{105.8 \, \text{m/s}} \)
7. \( \boxed{0.2 \, \text{m}} \)
8. \( \boxed{0.16 \, \text{Hz}} \)
9. \( \boxed{4800 \, \text{m/s}} \)
10. \( \boxed{5 \, \text{Hz}} \)
11. \( \boxed{12 \, \text{m}} \)
12. \( \boxed{212 \, \text{m/s}} \)
13. \( \boxed{6 \, \text{m}} \)
14. \( \boxed{348 \, \text{m/s}} \)