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14.Waves and Sound
hard
In Melde's experiment, the string vibrates in $4$ loops when a $50 \,gram$ weight is placed in the pan of weight $15\, gram.$ To make the string to vibrates in $6$ loops the weight that has to be removed from the pan is
A
$0.0007\, kg\, wt$
B
$0.0021\, kg\, wt$
C
$0.036 \,kg \,wt$
D
$0.0029 \,kg \,wt$
Solution
(c) Frequency of vibration of string is given by
$n = \frac{p}{{2l}}\sqrt {\frac{T}{m}} $==> $p\sqrt T = $constant ==> $\frac{{{p_1}}}{{{p_2}}} = \sqrt {\frac{{{T_2}}}{{{T_1}}}} $
Hence $\frac{4}{6} = \sqrt {\frac{{{T_2}}}{{(50 + 15)gm{\rm{ – }}force}}} $==> ${T_2} = 28.8\,gm{\rm{ – }}f$
Hence weight removed from the pan
$ = {T_1} – {T_2} = 65 – 28.8 = 3.62\,gm-force = 0.036 kg-f.$
Standard 11
Physics
