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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?

Respuesta :

mavila18

Answer:

n=2,3

Explanation:

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

[tex]f_n=\frac{nv_s}{2L}[/tex]

[tex]n=\frac{2Lf_n}{v_s}[/tex]

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

[tex]n_1=\frac{2(0.3m)(880Hz)}{340\frac{m}{s}}=2[/tex]

[tex]n_2=\frac{2(0.3m)(1320Hz)}{340\frac{m}{s}}=3[/tex]

Hope this helps!!