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When a stretched wire and a tuning fork are sounded together Y beats Per second are produced When length of wire is 90 cm or 100 cm frequency of the fork is 195 Hz Then Y = ?

Option: 1
9.75

Option: 2
11.42

Option: 3
8.26

Option: 4
7.25

Answers (1)

best_answer

Wire of length 90 cm frequency = n₁

wire of length 100 cm frequency = n₂

$n_1-n=Y\rightarrow (1)\,\,eq$

$n-n_2 =Y\rightarrow (2)\,\,eq$

(1) and (2) eq add

$n_1-n_2=2\,Y\rightarrow (3) \,\,eq$

$\frac{n_1}{n_2}=\frac{l_2}{l_1}=\frac{100}{90} \\$

$n_1=195 \\$

$\frac{195}{n_2}=\frac{100}{90}$

$100 \,n_2 =195 \times 90 \\$

$n_2 =\frac{195 \times 90}{100} \\$

$n_2 =\frac{39 \times 9}{2} \\$

$n_2 =\frac{351}{2}=175.5 \\$

$n_2 =175.5$

$n_1 \,\,and\,\,n_2$
put the value of eq (3)

$n_1-n_2=2 Y \\$

$195-175.5=2 Y\\$

$19.5=2 Y \\$

$Y=\frac{19.5}{2}=\frac{195}{20} \\$

$Y=9.75 \\$

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