Question

Figure shows three different modes of vibration of a string of length l.
(i) Which of the vibration is of largest amplitude?
(ii) Which of the vibration is of least frequency?
(iii) What is the ratio of frequency between (a) and (c)?
(iv) What is the ratio of wavelength between (b) and (a)

Answer 1

(i) : Vibration (b) has the largest amplitude.

(ii) : c vibrates in the fundamental mode. So, c has the least frequency.

(iii) : Frequency of (a), $f_a=\frac{3v}{32L}$

Frequency of (c), $f_c=\frac{v}{2L}$

$⟹\frac{f_a}{f_c}=3$

(iv) : Wavelength of (a), ${\lambda }_a=\frac{2}{3}L$

Wavelength of (b), ${\lambda }_b=L$

$⟹\frac{{\lambda }_b}{{\lambda }_a}=\frac{3}{2}$