An S-wave has a frequency of 3.6 Hz. The S-wave has a speed of 4.5 km/s. Calculate the wavelength of this S-wave. Use the Physics Equations Sheet.
How to approach this question
1. Identify the wave speed equation from the Physics Equations Sheet.
2. Check the units. The speed is in km/s, but the standard unit for the wave equation is m/s. You must convert the speed.
3. Rearrange the equation to make wavelength (λ) the subject.
4. Substitute the values for speed (v) and frequency (f).
5. Calculate the final answer and give the correct units.
Full Answer
1. Convert speed to m/s:
v = 4.5 km/s = 4.5 × 1000 m/s = 4500 m/s
2. Equation: wave speed (v) = frequency (f) × wavelength (λ)
3. Rearrange for wavelength (λ): λ = v / f
4. Substitute: λ = 4500 m/s / 3.6 Hz
5. Calculate: λ = 1250 m
The relationship between wave speed (v), frequency (f), and wavelength (λ) is given by the wave equation:
v = f × λ
We need to calculate the wavelength (λ), so we rearrange the equation:
λ = v / f
First, we must ensure the units are consistent. Frequency is in Hz (which is s⁻¹), so speed must be in m/s.
Given speed v = 4.5 km/s.
To convert km/s to m/s, we multiply by 1000:
v = 4.5 × 1000 m/s = 4500 m/s
Now substitute the values into the rearranged equation:
λ = 4500 m/s / 3.6 Hz
λ = 1250 m
Common mistakes
✗ Forgetting to convert the speed from km/s to m/s. This is a common mistake.\n✗ Rearranging the wave equation incorrectly (e.g., λ = f / v).\n✗ Calculation errors.
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