Understanding Standing Waves
A standing wave is formed by the interference of two waves traveling in opposite directions. In a string with three loops (or antinodes), we can analyze the relationship between the wavelength, the number of loops, and the amplitude.
Number of Loops and Wavelength
- In a standing wave, the number of loops or antinodes (points of maximum displacement) corresponds to a fraction of the wavelength.
- For a string with three loops:
- Each loop represents half of a wavelength (λ/2).
- Therefore, three loops represent 1.5 wavelengths (3 × λ/2).
Calculating the Wavelength
- The total length (L) of the string is equal to the number of half wavelengths:
\[
L = 3 \times \frac{\lambda}{2}
\]
- Rearranging gives us:
\[
\lambda = \frac{2L}{3}
\]
Amplitude and its Significance
- The amplitude (0.5 m in this case) refers to the maximum displacement of particles from their equilibrium position.
- It does not affect the wavelength directly, but it defines the energy of the wave.
- Higher amplitude indicates greater energy carried by the wave.
Conclusion
- In summary, the wavelength of the standing wave can be determined using the length of the string and the number of loops.
- The amplitude, while important for understanding wave behavior, does not influence the wavelength calculation directly.
This understanding is crucial for NEET aspirants as it covers fundamental wave properties essential for physics concepts.