An audio oscillator capable of producing notes of frequencies ranging from 500 Hz "to" 1500 Hz is placed constant tension T. The linear mass density of the wire is 0.75 g//m. It is observed that by varying the frequency of the oscillator over the given permissible rang the sonometer wire sets into vibration at frequencies 840 Hz and 1120 Hz. a. Find the tension in the string . b. What are the frequencies of the first and fourth overtone produced by the vibrating string?

An audio oscillator capable of producing notes of frequencies ranging

1.	An audio oscillator capable of producing notes of frequencies ranging from 500 Hz "to" 1500 Hz is placed constant tension T. The linear mass density of the wire is 0.75 g//m. It is observed that by varying the frequency of the oscillator over the given permissible rang the sonometer wire sets into vibration at frequencies 840 Hz and 1120 Hz. a. Find the tension in the string . b. What are the frequencies of the first and fourth overtone produced by the vibrating string?
Answer» Solution :a. `(f)/(f') = (840)/(1120) = (3)/(4)` In the frequency of the fundamental note `= f_(0)` `:. F_(0) = (1)/( 2l) sqrt((T)/( mu))` where `f_(0) = (840)/(3) = 280 HZ` or `T = 4 l^(2) mu f_(0)^(2) = 4 (0.25)^(2) xx (0.75 xx 10^(-3)) xx (280)^(2)` ` = 14.7 N` b. Frequency of the FIRST overtone ` = 2 f_(0) = 2 xx 280 = 560 Hz` and that of fourth overtone ` = 5 f_(0) = 5 xx 280 = 140 Hz`