Question

der a string stretched between two supports. The speed of the propagation of transverse waves is 85 m/s, and two successive standing-wave frequencies are 510 Hz and 680 Hz.a) What is the the order of these two harmonics (first, second, etc)?b) What is the length of the string?

Answer 1

a) 3, 4

b)0.25 m

Step-by-step explanation:

Given frequency f_1= 510 Hz

and frequency f_2= 680 Hz

v= 85 m/s

`f_n= (nv)/(2L)`

and

`f_(n+1)= ((n+1)v)/(2L)`

therefore,

`f_(n+1)-f_n= ((n+1)v)/(2L)-(nv)/(2L)`

= v/2L

`L= (v)/(2(f_(n+1)-f_1))`

`L= (85)/(2(680-510))`

Therefore, length of the string = 0.25 m

510 = 85n/2×0.25

n= 3

therefore order of two harmonics 3,4 .