Question on Frequencies at different Resonance

Waves and Sounds is one of the basic concept in Physics which deals with wavelength, frequency and velocity of waves and sounds under uniform motion. Initial Frequency generated by any instrument is called as fundamental frequency and sound harmonics.

Topic : Vibrating String with a property of Resonance

Resonance is the tendency of an instrument to vibrate with large amplitude.

Question : A particular string resonates in four loops at a frequency of 280 Hz. Name at least three other frequencies at which it will resonate.

Solution :

Four loops means four anti-nodes, which means that we have the fourth harmonic, as the fundamental is one "loop" or anti-node.

The fourth harmonic would be four times the fundamental, so therefore the fundamental is 280 Hz/4 = 70 Hz,

and the next two would be 140 Hz, and 210 Hz.

So f₁ = 70Hz (fundamental frequency)
f₂ = 2f₁ = 2 x 70 = 140 Hz
f₃ = 3f₁ = 3 x 70 = 210 Hz
f₄ = 4f₁ = 4 x 70 = 280 Hz

For more explanations related to the concept can be found in physics help or science help.