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The diagram below illustrates a standing wave on a string of length 4.99 m which is clamped at both ends. What is the wavelength of the standing wave?


To find the wavelength of the standing wave shown in the diagram, we need to identify how many complete wavelengths fit along the length of the string. Here’s a step-by-step outline:

1. **Count the Nodes**: Each point where the wave crosses the horizontal axis and doesn’t move is a node. Nodes in a standing wave occur at regular intervals and separate each half-wavelength.

2. **Identify the Pattern**: It appears that there are 10 full loops (or antinodes) along the length of the string, with nodes at each end, which indicates 5 complete wavelengths.

3. **Calculate the Wavelength**:
   \[
   \text{Wavelength} = \frac{\text{Length of string}}{\text{Number of wavelengths}}
   \]
   Since the string length is \(4.99 \, \text{m}\) and it accommodates 5 full wavelengths, the wavelength \(\lambda\) is:
   \[
   \lambda = \frac{4.99 \, \text{m}}{5} = 0.998 \, \text{m}
   \]

So, the wavelength of the standing wave is approximately \(0.998 \, \text{m}\).

Would you like more details on this solution or have any questions? 

Here are some related questions for further exploration:
1. How does the frequency of a standing wave change if the string length is doubled?
2. What factors influence the speed of waves on a string?
3. How are standing waves created, and what conditions are necessary?
4. If the frequency of the wave is known, how can we find the wave speed?
5. How would the pattern change if the string was fixed at only one end?

**Tip**: Remember, the number of loops or antinodes is twice the number of wavelengths in a standing wave setup with both ends fixed.

The diagram below illustrates a standing wave on a string of length 4.99 m which is clamped at both ends. What is the wavelength of the standing wave?

Learn how to calculate the wavelength of a standing wave on a string of length 4.99 m clamped at both ends. This problem involves wave mechanics concepts, including standing waves, wavelength calculations, and standing wave conditions. Suitable for Grades 10-12 students.

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