Wavelength
For a standing transverse wave in a stretched string that is attached at both ends, the number of the normal mode equals the number of half wavelengths that are contained in its length. The wavelength of the th normal mode is therefore
where denotes the string's length.
In the question, you are given and . Substitute to obtain the numerical answer for the wavelength.
Frequency
The frequency of the standing wave in the th normal mode, which is the th harmonic , can be found using the relation that is valid for all periodic waves
where is the wavelength of the th normal mode (see the formula for wavelength) and is the speed of transverse waves in the string. This speed is not given directly, but can be obtained from the formula
where is the given tension in the string and and are its given mass and length, respectively. Perform all necessary substitutions to obtain the frequency in terms of given quantities.
For the value of the fourth harmonic,
You haw a uniform string with a mass of 0.0130 kg and length 1.75 m under...
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