Wave calculations|KS4 Physics|Teachit - Free Printable

Problem: Calculate the speed of each wave using the equation below:

$$
\text{wave speed } v = \text{frequency } f \times \text{wavelength } \lambda
$$
Remember to use the correct units (e.g., wave speed in m/s, frequency in Hz, and wavelength in meters).

#### Given tasks:
1. Frequency $ f = 10 \, \text{Hz} $ and wavelength $ \lambda = 3 \, \text{m} $.
2. Wavelength $ \lambda = 5 \, \text{m} $ and frequency $ f = 4 \, \text{Hz} $.
3. Frequency $ f = 500 \, \text{kHz} $ and wavelength $ \lambda = 25 \, \text{cm} $.
4. Wavelength $ \lambda = 3.000 \, \text{m} $ and frequency $ f = 150 \, \text{Hz} $.
5. Frequency $ f = 30 \, \text{Hz} $ and wavelength $ \lambda = 10 \, \text{m} $.
6. Half the wavelength of the wave in question (c) and a frequency of $ 4 \, \text{Hz} $.
7. Wavelength $ \lambda = 50 \, \text{cm} $ and frequency $ f = 4 \, \text{Hz} $. Give the units in meters per second.

---

Solution:

#### Task 1:
- Frequency $ f = 10 \, \text{Hz} $
- Wavelength $ \lambda = 3 \, \text{m} $

Using the formula:
$$
v = f \times \lambda
$$
Substitute the values:
$$
v = 10 \, \text{Hz} \times 3 \, \text{m} = 30 \, \text{m/s}
$$

Answer for Task 1:
$$
\boxed{30 \, \text{m/s}}
$$

---

#### Task 2:
- Wavelength $ \lambda = 5 \, \text{m} $
- Frequency $ f = 4 \, \text{Hz} $

Using the formula:
$$
v = f \times \lambda
$$
Substitute the values:
$$
v = 4 \, \text{Hz} \times 5 \, \text{m} = 20 \, \text{m/s}
$$

Answer for Task 2:
$$
\boxed{20 \, \text{m/s}}
$$

---

#### Task 3:
- Frequency $ f = 500 \, \text{kHz} = 500 \times 10^3 \, \text{Hz} = 5 \times 10^5 \, \text{Hz} $
- Wavelength $ \lambda = 25 \, \text{cm} = 25 \times 10^{-2} \, \text{m} = 0.25 \, \text{m} $

Using the formula:
$$
v = f \times \lambda
$$
Substitute the values:
$$
v = (5 \times 10^5 \, \text{Hz}) \times (0.25 \, \text{m}) = 1.25 \times 10^5 \, \text{m/s}
$$

Answer for Task 3:
$$
\boxed{1.25 \times 10^5 \, \text{m/s}}
$$

---

#### Task 4:
- Wavelength $ \lambda = 3.000 \, \text{m} $
- Frequency $ f = 150 \, \text{Hz} $

Using the formula:
$$
v = f \times \lambda
$$
Substitute the values:
$$
v = 150 \, \text{Hz} \times 3.000 \, \text{m} = 450 \, \text{m/s}
$$

Answer for Task 4:
$$
\boxed{450 \, \text{m/s}}
$$

---

#### Task 5:
- Frequency $ f = 30 \, \text{Hz} $
- Wavelength $ \lambda = 10 \, \text{m} $

Using the formula:
$$
v = f \times \lambda
$$
Substitute the values:
$$
v = 30 \, \text{Hz} \times 10 \, \text{m} = 300 \, \text{m/s}
$$

Answer for Task 5:
$$
\boxed{300 \, \text{m/s}}
$$

---

#### Task 6:
- Half the wavelength of the wave in question (c).
- Frequency $ f = 4 \, \text{Hz} $.

From Task 3, the wavelength $ \lambda = 0.25 \, \text{m} $. Half of this wavelength is:
$$
\lambda_{\text{half}} = \frac{0.25 \, \text{m}}{2} = 0.125 \, \text{m}
$$

Using the formula:
$$
v = f \times \lambda
$$
Substitute the values:
$$
v = 4 \, \text{Hz} \times 0.125 \, \text{m} = 0.5 \, \text{m/s}
$$

Answer for Task 6:
$$
\boxed{0.5 \, \text{m/s}}
$$

---

#### Task 7:
- Wavelength $ \lambda = 50 \, \text{cm} = 50 \times 10^{-2} \, \text{m} = 0.5 \, \text{m} $
- Frequency $ f = 4 \, \text{Hz} $

Using the formula:
$$
v = f \times \lambda
$$
Substitute the values:
$$
v = 4 \, \text{Hz} \times 0.5 \, \text{m} = 2 \, \text{m/s}
$$

Answer for Task 7:
$$
\boxed{2 \, \text{m/s}}
$$

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Final Answers:

1. $\boxed{30 \, \text{m/s}}$
2. $\boxed{20 \, \text{m/s}}$
3. $\boxed{1.25 \times 10^5 \, \text{m/s}}$
4. $\boxed{450 \, \text{m/s}}$
5. $\boxed{300 \, \text{m/s}}$
6. $\boxed{0.5 \, \text{m/s}}$
7. $\boxed{2 \, \text{m/s}}$