Question

calculating wave speed, frequency and λ 5
name
date
period 1 ② 3 4

1. what is the v if λ = 8 m and f = 20 hz?
2. what is the λ if v = 50 m/s and f = 25 hz?
3. what is the f if v = 50 m/s and λ = 10 m?
4. what is the v if λ = 1 m and f = 345 hz?
5. what is the λ if v = 100 m/s and f = 3 hz?
6. what is the f if v = 120 m/s and λ = 3 m?
7. what is the v if λ = 3 m and f = 10 hz?
8. what is the λ if v = 345 m/s and f = 790 hz?
9. what is the f if v = 345 m/s and λ = .25 m?

Explanation:

To solve these problems, we use the wave speed formula: \( v = \lambda \cdot f \), where:

• \( v \) = wave speed (in m/s)
• \( \lambda \) = wavelength (in m)
• \( f \) = frequency (in Hz)

We can rearrange the formula to solve for the unknown variable:

• To find \( v \): \( v = \lambda \cdot f \)
• To find \( \lambda \): \( \lambda = \frac{v}{f} \)
• To find \( f \): \( f = \frac{v}{\lambda} \)

Problem 9: What is \( v \) if \( \lambda = 8 \, \text{m} \) and \( f = 20 \, \text{Hz} \)?

Step 1: Identify the formula

We use \( v = \lambda \cdot f \)

Step 2: Substitute the values

\( \lambda = 8 \, \text{m} \), \( f = 20 \, \text{Hz} \)
\( v = 8 \, \text{m} \times 20 \, \text{Hz} \)

Step 3: Calculate

\( v = 160 \, \text{m/s} \)

Answer:

\( 160 \, \text{m/s} \)

Problem 10: What is \( \lambda \) if \( v = 50 \, \text{m/s} \) and \( f = 25 \, \text{Hz} \)?

Step 1: Identify the formula

We use \( \lambda = \frac{v}{f} \)

Step 2: Substitute the values

\( v = 50 \, \text{m/s} \), \( f = 25 \, \text{Hz} \)
\( \lambda = \frac{50 \, \text{m/s}}{25 \, \text{Hz}} \)

Step 3: Calculate

\( \lambda = 2 \, \text{m} \)