Question

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

• A. 205 Hz
• B. 195 Hz
• C. 200 Hz
• D. 210 Hz

Answer 1

The correct option is A 205 Hz

We know that,

$beats=(\nu +{\nu }^{\prime })$

So for the first case,

$(\nu \pm 200)=5$

So this gives,

$\nu =205Hz$ or $\nu =195Hz$ ...(i)

For the 2nd case,

$(2\nu \pm {\nu }^{\prime })=10$

$(2\nu \pm 420)=10$

$2\nu =430Hz$ or $2\nu =410Hz$ ...(ii)

Now, by substituting the value of $\nu$ from equation (i) and checking which one satisfy equation (ii)

So, taking $\nu =205Hz$

$2\nu =410Hz$, which satisfies equation (ii)

But when we take, $\nu =195Hz$

$2\nu =390Hz$, which doesn’t satisfy equation (ii)

So the value of $\nu =205Hz$

Hence, option (A) is correct