Waves on a String With No End
In the top left box, choose “Oscillate.” In the top right box, choose “No End.” Set the damping to “None” at the bottom. Finally, check the box next to “Rulers” on the lower right.
Your goal in this first part of the lab is to determine the speed of the waves on the string for each tension setting (high, medium and low). Use the knowledge gained during your Chapter 16 quest to calculate these speeds.
| Tension | Speed (cm/s) |
| High | |
| Medium | |
| Low |
Please explain how you made these speed calculations and the measurements you had to make to do so:
The Correct Answer and Explanation is :
To calculate the speed of waves on a string for each tension setting (high, medium, and low), we need to apply the basic wave speed formula for waves on a string:
[
v = \sqrt{\frac{T}{\mu}}
]
Where:
- (v) is the wave speed (in cm/s),
- (T) is the tension in the string (in dynes or Newtons, but we use relative values for simplicity here),
- (\mu) is the mass per unit length of the string (in g/cm or kg/m).
Step 1: Measuring Tension and Wave Speed
In the lab, the string is set to oscillate without any ends, meaning the waves will continue indefinitely. The “tension” can be varied by adjusting the setting to high, medium, and low. These tension settings typically correspond to changes in the force applied to the string, which alters the wave speed.
Step 2: Determine the Wave Speed for Each Tension Setting
- High Tension: Set the string to high tension and generate a standing wave. Measure the distance between the nodes or the wavelength of the wave. Once the wavelength is known, measure the frequency of oscillation (how many complete oscillations occur in one second, i.e., the frequency, (f)). Using the wave equation (v = f \times \lambda), where (\lambda) is the wavelength and (f) is the frequency, you can calculate the wave speed.
- Medium Tension: Repeat the same process with the medium tension setting, ensuring the same method is applied to measure frequency and wavelength.
- Low Tension: For the low tension setting, measure the wavelength and frequency again, then use the same formula to determine the wave speed.
Step 3: Using the Formula to Calculate the Speed
Once the tension values are known (relative to high, medium, and low settings), the mass per unit length (\mu) can be approximated from the properties of the string, or if it’s consistent for all measurements, we may simply observe that the wave speed increases with tension.
Final Calculation
For each tension setting:
- Measure the wave’s frequency ((f)) and wavelength ((\lambda)),
- Use the wave speed formula to find (v = f \times \lambda) for each setting (high, medium, and low).
In the context of the lab, the wave speed increases with increasing tension because the force acting on the string (tension) increases.