Question

Forty-one forks are so arranged that each produced $5$ beats per second when sounded with its near fork. If the frequency of last fork is double the frequency of first fork, then the frequencies of the first and last fork, respectively are:

• A. $200,400$
• B. $205,410$
• C. $195,390$
• D. $100,200$

Answer 1

The correct option is A $200,400$

Each fork gives $5$ beats with the preceding ones. So, all are in A.P. with common difference of $5$

$a=$ Frequency

$a,a+5,a+10,........a_{41}$

$a_{41}=a+(41-1)5$

$\Rightarrow a_{41}=a+200$

Given,

$a_{41}=2a$

$\Rightarrow 2a=a+200$

$\Rightarrow a=200$

So, least or First Fork Frequency $=200$

Last Fork Frequency $=200+200=400$