A source of frequency gives 5 beats/second when sounded with a so… - Vidyadip

MCQ

A source of frequency $\nu$ gives $5$ beats/second when sounded with a source of frequency $200 \;Hz$. The second harmonic of frequency $2\nu$ of source gives $10$ beats/second when sounded with a source of frequency $420\; Hz$. The value of $v$ is .... $Hz$

A
$195$
✓
$205$
C
$200$
D
$210$

✓

Answer

Correct option: B.

$205$

b
(b) Initially number of beats per second $= 5$

$ \therefore$ Frequency of pipe $= 200 \pm \,5 = 195 Hz$ or $205 Hz$ ...$(i)$

Frequency of second harmonics of the pipe $= 2n$

and number of beats in this case $= 10$

$ \therefore$ $2n = 420 \pm \, 10 $

==> $410 Hz$ or $430 Hz$

==> $n = 205 Hz$ or $215 Hz$ ... $(ii)$

From equation $(i)$ and $(ii)$ it is clear that $n = 205 Hz$

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