Question

A 30 cm violin string is placed in front of a speaker, and the frequency of a sine wave generator driving the speaker is slowly swept from 500 Hz to 1500 Hz. During the time the frequency is changing, the string noticeably vibrates only twice: once at 880 Hz and once at 1320 Hz. Which resonant modes of the string are these?

Answer 1

n=2,3

Step-by-step explanation:

We have to take into account the expression for the fundmentals modes in a vibrating cord

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

`n=(2Lf_n)/(v_s)`

in this case we have resonant at 880Hz and 1320Hz

`n_1=(2(0.3m)(880Hz))/(340(m)/(s))=2`

`n_2=(2(0.3m)(1320Hz))/(340(m)/(s))=3`

Hope this helps!!