A Level Physics Practice Exam

For the first harmonic, how is the wavelength related to the length (L)?

1. Wavelength equals L

2. Wavelength equals 2L

3. Wavelength equals L/2

4. Wavelength equals 3L

The correct answer is: Wavelength equals 2L

In the context of standing waves on a string fixed at both ends, the first harmonic, also known as the fundamental frequency, corresponds to the configuration where the string vibrates in its simplest mode. In this mode, one full wavelength fits into the length of the string. The relationship between the wavelength and the length of the string for the first harmonic is such that the length of the string is half the wavelength. This can be understood through the observation that the first harmonic has a node at each fixed end of the string and a single antinode in the center. Because the length of the string is L, you can see that the full wavelength, which is represented by the distance from one node to the next, is twice the length of the string. Therefore, we express this relationship mathematically as: Wavelength = 2L. This foundational concept is crucial in understanding wave phenomena, especially in contexts involving standing waves on strings or tubes.