find the ratio of frequency of fundamental tone and first overtone in a stretched spring
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The ratio of frequencies produced by stretched string in case of consecutive harmonic is given by 1 : 2 : 3 : 4 ..... etc
[ Because frequency of nth harmonic is given by v = n/2l√{T/m}, here l is length of string , T is tension in string , m is mass per unit length , so for 1st harmonic ,v = 1/2l√{T/m} , 2nd harmonic , v = 2/2l√{T/m} etc...]
fundamental tone means first harmonic , And first overtone means 2nd harmonic
So, ratio of first and 2nd harmonic = 1 : 2
hence, ratio of frequencies of fundamental tone and first overtone = 1/2 or 1 : 2
[ Because frequency of nth harmonic is given by v = n/2l√{T/m}, here l is length of string , T is tension in string , m is mass per unit length , so for 1st harmonic ,v = 1/2l√{T/m} , 2nd harmonic , v = 2/2l√{T/m} etc...]
fundamental tone means first harmonic , And first overtone means 2nd harmonic
So, ratio of first and 2nd harmonic = 1 : 2
hence, ratio of frequencies of fundamental tone and first overtone = 1/2 or 1 : 2
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