Questions: Question 1 A wire of length L is fixed at both ends. Which of the options below represents the stationary wave with the longest wavelength that can be established in this wire?

Question 1 A wire of length L is fixed at both ends. Which of the options below represents the stationary wave with the longest wavelength that can be established in this wire?

Transcript text: Question 1 A wire of length $L$ is fixed at both ends. Which of the options below represents the stationary wave with the longest wavelength that can be established in this wire?

Solution

Solution Steps

Step 1: Understand the relationship between wavelength and frequency

The wavelength of a standing wave is inversely proportional to its frequency. This means the longest wavelength corresponds to the lowest frequency, which is the fundamental frequency or first harmonic.

Step 2: Visualize the first harmonic

The first harmonic of a standing wave fixed at both ends has only one antinode (the point of maximum displacement) in the middle and two nodes (points of zero displacement) at the ends. This resembles half of a sine wave.

Step 3: Identify the correct option

The third option from the top depicts a single curve similar to half a sine wave. This corresponds to the first harmonic.