Waves Ques 33
33. In a guitar, two strings $A$ and $B$ made of same material are slightly out of tune and produce beats of frequency $6$ $ Hz$. When tension in $B$ is slightly decreased, the beat frequency increases to $7 $ $Hz$. If the frequency of $A$ is $530 $ $Hz$, the original frequency of $B$ will be
[2020]
(a) $524 $ $Hz$
(b) $536 $ $Hz$
(c) $537 $ $Hz$
(d) $523 $ $Hz$
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Answer:
Correct Answer: 33.(a)
Solution:
- (a) Frequency of string, $f=\frac{1}{2 l} \sqrt{\frac{T}{m}}$
Frequency $\propto \sqrt{\text{ Tension }}$
Difference of $f_A$ and $f_B$ is $6$ $ Hz$.
If tension decreases, $f_B$ decreases and becomes $f^{\prime} _{B}$.
Now, difference of $f_A$ and $f^{\prime} _{B}=7 $ $Hz$ (increases)
So, $f_A>f_B$
$f_A-f_B=6$ $ Hz$
$\Rightarrow f_A=530$ $ Hz \Rightarrow f_B=524 $ $Hz$ (original)
BETA
