Question

A string is stretched between fixed supports separated by 1.3 m. It is observed to have resonant frequencies of 579 and 347 Hz, and no other resonant frequencies between these two. What is the wave speed for this string? Give your answer in Standard SI units.

(THIS TYPE OF QUESTION IS ALREADY ANSWERED *I KNOW* PLEASE EXPLAIN EACH AND EVERRY FORMULA AND CORECT ANSWER FOR IT.) THANKS A LOT

Answer 1

a) The resonant wavelengths have the general formula ( 2*L/n )

So we put wavelength 1 (w1 ) = 2L / n and w2 will be 2L /(n+1)

f1 = c / w1 and f2 = c / w2

then

f1*w1 = f2*w2

347*2*1.3/n = 579 *2*1.3 / (n+1)

347 *( n + 1) = 579 *n

n = 347 /( 579 – 347) = 1.5

= 2 (aprox)

Therefore 347 is the 2nd harmonic
The first harmonic ( the fundamental, the lowest resonant frequency) must be 347 /2 = 173.5 Hz

b) wave speed = f * w = 173.5 *2*L

= 173.5*2*1.3

= 451.1 m/s