A steel wire of mass and length is fixed at the two ends. The tension in the wire is . Find the frequency and wavelength of the fourth harmonic of the fundamental.
Step 1 Given data.
Mass of a steel wire,
Length of the wire,
Tension in the wire,
Step 2: Finding the frequency.
We know that,
Where, is fundamental frequency, is the speed of the wave.
And,
Where, is the tension and is mass per unit length.
Step 3: Finding the frequency of the fourth harmonic of the fundamental.
Where is the harmonic frequency, is the number of harmonic, is the fundamental frequency.
At ,
Then, the frequency of 4th harmonic.
Step 4: Finding the wavelength of the fourth harmonic of the fundamental.
As we know,
Where fourth harmonic wavelength, is speed of the fourth harmonic wave.
Hence, the frequency of the fourth harmonic is and the wavelength of the fourth harmonic of the fundamental is .