A guitar string 0.65m long vibrates with a first harmonic frequency of 280Hz. Mary measures 1m of the string and discovers that it weighs 8.0x10^-4 kg. What is the tension in the guitar string?
f = 280 Hz, l = 0.65 m, μ = 8x10^-4 kgm^-1Therefore use the equation f=(1/2l)(T/μ)^1/2Rearrange it to get it in the form T= by multiplying f by 2l, squaring both sides and then multiplying by μ to getT = μ*(2lf)^2(This can also be simplified to T = 4μl^2f^2 )Then simply plug in the numbers that we gathered from the questionT = 48x10^-40.65^2280^2T = 48x10^-40.422578400T = 105.9968 NThe numbers in the question were to two significant figures, so round to two significant figuresT = 110 N
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