Use your understanding of the length-wavelength relationships for the various harmonics and basic wave equations to solve the following problems.
Consider the diagram at the right of a resonating string. If the string has a length of 76.4 cm, then the wavelength is ______ cm.
Wavelength
cm
The frequency of the first harmonic of a string is 399 Hz. Determine the frequency of ....
... the second harmonic of the same string.
Frequency of 2nd Harmonic
Hz
... the sixth harmonic of the same string.
Frequency of 6th Harmonic
... the first harmonic of a string which is 2.9 times as long.
New 1st Harm. Frequency
... the fourth harmonic of a string which is two-fifths the length.
New 4th Harm. Frequency
In a demonstration, Mr. H stretches a steel wire to a length of 1.59 meters and braces both ends so that they are not free to vibrate. He attaches a fancy piece of equipment which he calls a mechanical oscillator to the wire and explains how it works. Then Mr. H turns the oscillator on and tunes the frequency to 670 Hz. To the amazement of the class, the wire begins vibrating in the sixth harmonic wave pattern.
Determine the speed of waves within the wire.
Speed
m/s
Determine the frequency at which the wire will vibrate with the first harmonic wave pattern.
Frequency of 1st Harmonic
Determine the frequency at which the wire will vibrate with the second harmonic wave pattern.
Olivia and Mason are doing a lab which involves stretching an elastic cord between two poles that are 80.4 cm apart. They use a mechanical oscillator to force the cord to vibrate with the third harmonic wave pattern when the frequency is 60 Hz. Determine the speed of vibrations within the elastic cord.
A steel piano wire is pulled to a tension of 455 N and has a mass density of 0.00601 kg/m. The string is 56.0 cm long and vibrates at its fundamental frequency.
Determine the speed at which vibrations travel through the wire.
Determine the wavelength of the standing wave pattern for the fundamental frequency.
m
Determine the frequency of its vibrations.
Frequency
Anna Litical and Noah Formula (the Physics Dream Team, as their friends refer to them) are doing a Physics lab with a 82.5 cm long wire that has a linear density of 0.415 g/m. They pull the wire to a tension of 335 N.
What frequency must their wire be vibrated with to form the 5th harmonic standing wave pattern?
Frequency of 5th Harmonic
Determine the fundamental frequency of the wire when held at this tension.
Fundamental Frequency