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!
 

Thread 'Errors and significant figures'

I multiplied the values first without the error limit. Got 19.38. rounded it off to 2 significant figures since the given data has 2 significant figures. So = 19. For error I used the above formula. It comes out about 1.48. Now my question is. Should I write the answer as 19±1.5 (rounding 1.48 to 2 significant figures) OR should I write it as 19±1. So in short, should the error have same number of significant figures as the mean value or should it have the same number of decimal places as...
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Thread 'A cylinder connected to a hanging mass'

Thread 'A cylinder connected to a hanging mass'

Let's declare that for the cylinder, mass = M = 10 kg Radius = R = 4 m For the wall and the floor, Friction coeff = ##\mu## = 0.5 For the hanging mass, mass = m = 11 kg First, we divide the force according to their respective plane (x and y thing, correct me if I'm wrong) and according to which, cylinder or the hanging mass, they're working on. Force on the hanging mass $$mg - T = ma$$ Force(Cylinder) on y $$N_f + f_w - Mg = 0$$ Force(Cylinder) on x $$T + f_f - N_w = Ma$$ There's also...
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