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

Answer:

n=2,3

Explanation:

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

$f_n=\frac{nv_s}{2L}$

$n=\frac{2Lf_n}{v_s}$

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

$n_1=\frac{2(0.3m)(880Hz)}{340\frac{m}{s}}=2$

$n_2=\frac{2(0.3m)(1320Hz)}{340\frac{m}{s}}=3$

Hope this helps!!