Calculating Fundamental Frequency and Wavelength of a Vibrating String

AI Thread Summary
To calculate the fundamental frequency of a 90 cm long steel string under 200N tension with a linear density of 1.1g/m, the formula f = 1/2L * sqrt(T/μ) is used. The initial calculation yields a frequency of 7.49 Hz. However, the user realizes that the linear density must be converted from grams to kilograms for accurate results. The speed of sound in air is then applied to find the wavelength, but the initial answer is incorrect due to unit conversion errors. Correcting these units is essential for obtaining the right wavelength of the sound wave.
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Homework Statement



A 90 cm long steel string with a linear density of 1.1g/m is under 200N tension. It is plucked and vibrates at its fundamental frequency. What is the wavelength of the sound wave that reaches your ear in a 20 degree C room?

Homework Equations



f = 1/2L * sqrt T/mu
v = f*gamma

The Attempt at a Solution


1/(2*0.9) * sqrt (200/1.1) = 7.49Hz
v = f*gamma so v/f = gamma; 343m/s/7.49 Hz = 45.78m
but this answer is wrong! Where did I go wrong?
 
Physics news on Phys.org
metric units?
 
yes, all metric
 
what is the metric unit for mass?
 
do I need to convert grams to kilograms?
 
yup. thanks!
 
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