Question
11.3 A wave that moves at the speed of 100 \( \mathrm{~m} \cdot \mathrm{~s}^{-1} \), has a wavelength of 40 m . Calculate the frequency.
Ask by Barnett Mckenzie. in South Africa
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The frequency of the wave is 2.5 Hz.
Solution
To calculate the frequency \( f \) of a wave, you can use the relationship between wave speed \( v \), wavelength \( \lambda \), and frequency \( f \):
\[
v = \lambda \times f
\]
Solving for frequency:
\[
f = \frac{v}{\lambda}
\]
**Given:**
- Wave speed \( v = 100 \ \mathrm{m/s} \)
- Wavelength \( \lambda = 40 \ \mathrm{m} \)
**Calculation:**
\[
f = \frac{100 \ \mathrm{m/s}}{40 \ \mathrm{m}} = 2.5 \ \mathrm{Hz}
\]
**Answer:**
The frequency of the wave is **2.5 Hz**.
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Simplify this solution Beyond the Answer
To find the frequency of the wave, you can use the wave speed formula: \( v = f \times \lambda \), where \( v \) is the speed of the wave, \( f \) is the frequency, and \( \lambda \) is the wavelength. In this case, you have \( v = 100 \, \mathrm{m/s} \) and \( \lambda = 40 \, \mathrm{m} \). Rearranging the formula to solve for frequency gives you: \[ f = \frac{v}{\lambda} \] Substituting in the values: \[ f = \frac{100 \, \mathrm{m/s}}{40 \, \mathrm{m}} = 2.5 \, \mathrm{Hz} \] So, the frequency of the wave is 2.5 Hz.
