# physics

A 1.6-m-long string fixed at both ends vibrates at resonant frequencies of 792 Hz and 990 Hz, with no other resonant frequency between these values.

(a) What is the fundamental frequency of this string?

(b) When the tension in the string is 1165 N, what is the total mass of the string?

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1. f1 is the fundamental frequency. Resonant frequencies are
f(n) = n•f1 = 792 Hz,
f(n+1) =(n+1) •f1= 990 Hz
f(n)/f(n+1) = n/(n+1) = 792/990.
n = 4,
f1 =f(n)/n = 792/4 = 198 Hz,
f1 = v/2•L ,
v = f1•2•L = 198•2•1.6 = 633.6 m/s,
v = sqrt(T/m(o)),
m(o) = m/L,
m =T•L/v^2 = 1165•1.6/(633.6)^2 = 4.23•10^-3 kg =4.23 g.

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