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Bot GPT 4-o mini To address your questions, let's break each part down clearly.
### a) Amplitude and Wavelength Measurement
**Amplitude Measurement:**
- **Definition:** The amplitude is the maximum displacement of points on a wave from its rest position (equilibrium).
- **Measurement:** To measure the amplitude, you would look at the vertical distance from the equilibrium position (the midline of the wave) to the crest (the highest point) or to the trough (the lowest point).
- **Sketch:** If you were to sketch this, it would look like a wave where you draw a horizontal line in the middle (the rest position) and then show the distance from this line to the peak and the lowest point.
**Wavelength Measurement:**
- **Definition:** Wavelength is the distance between two consecutive points that are in phase on the wave, usually measured from crest to crest or trough to trough.
- **Measurement:** For the given wave from point X to point Y, you would measure the distance between two consecutive crests (or troughs) of the wave.
- **Provided Information:** In this case, you have indicated that the wavelength from X to Y is 4.8 meters.
### b) Wavelength in Metres
Since you have already provided the information that the wavelength from X to Y is **4.8 meters**, that is the answer.
### c) Wave Speed and Frequency
**Wave Speed Calculation:**
- To find the speed of the wave, we can use the formula:
\[
\text{Speed} = \frac{\text{Distance}}{\text{Time}}
\]
- The distance in one wavelength is 4.8 m, and the time taken from point X to point Y is 6.0 s. Therefore,
\[
\text{Speed} = \frac{4.8 \, \text{m}}{6.0 \, \text{s}} = 0.8 \, \text{m/s}
\]
**Frequency Calculation:**
- The frequency can be calculated using the relation between speed, frequency, and wavelength:
\[
\text{Speed} = \text{Frequency} \times \text{Wavelength}
\]
- Rearranging gives:
\[
\text{Frequency} = \frac{\text{Speed}}{\text{Wavelength}} = \frac{0.8 \, \text{m/s}}{4.8 \, \text{m}} \approx 0.167 \, \text{Hz}
\]
### d) Speed and Wavelength at 2.0 Hz Frequency
**New Wave Speed Calculation:**
- If the frequency of the source changed to **2.0 Hz**, we can find the speed using the wavelength which remains the same as we are interested in the effects of changing frequency:
- Using the previously given wavelength (4.8 m),
\[
\text{Speed} = \text{Frequency} \times \text{Wavelength} = 2.0 \, \text{Hz} \times 4.8 \, \text{m} = 9.6 \, \text{m/s}
\]
**New Wavelength Calculation:**
- The relation between speed, frequency, and wavelength can be rearranged as:
\[
\text{Wavelength} = \frac{\text{Speed}}{\text{Frequency}} = \frac{9.6 \, \text{m/s}}{2.0 \, \text{Hz}} = 4.8 \, \text{m}
\]
Thus, the wavelength remains **4.8 m**, even with the change in frequency.
### Summary:
- Amplitude and wavelength can be measured based on specific wave features.
- The wave speed with the initial conditions is 0.8 m/s, and frequency is approximately 0.167 Hz.
- At a frequency of 2.0 Hz, the speed would be 9.6 m/s, while the wavelength stays the same at 4.8 m.
anonymous
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