What are the three longest wavelengths for standing waves on...

What are the three longest wavelengths for standing waves on a 240 -cm-long string that is fixed at both ends?
b. If the frequency of the second-longest wavelength is $50.0 \mathrm{Hz},$ what is the frequency of the third-longest wavelength?

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Standing Waves on a String

Standing waves are created on a string when two waves of the same frequency and amplitude travel in opposite directions, leading to fixed nodes along the string due to interference. In a string fixed at both ends, the boundary conditions require that the waves have nodes at the endpoints, which restricts the wavelengths that can form standing waves.

Harmonics

Harmonics refer to the specific set of frequencies and wavelengths that satisfy the standing wave conditions on a string fixed at both ends. The lowest frequency is called the fundamental mode (first harmonic), and its wavelength is twice the length of the string. Higher harmonics (second, third, etc.) have wavelengths that are fractions of the fundamental wavelength, typically expressed as ? = 2L/n, where n is an integer.

Frequency-Wavelength Relationship

The relationship between frequency, wavelength, and wave speed is given by the equation f = v/?, where f is frequency, v is the wave speed, and ? is the wavelength. For a string under tension, wave speed is constant, so changes in the wavelength of the standing wave directly affect its frequency. This concept helps in determining how the frequencies of different harmonics scale with each other.

Transcript

Please give Ace some feedback