Question

A set of $48$ tuning forks is arranged in a series of descending frequencies such that each fork gives $4$ beats per second with preceding one. The frequency of first fork is $1.5$ times the frequency of the last fork, find the frequency of the first and ${42}^{nd}$ tuning fork.

Answer 1

Give that

$n_1=1.5n_{48}$ beat frequence $=4Hz$

The set of turning forks are arranged in decreasing order of frequencies

$\therefore n_2=n_1-4:n_3=n_2-4$

$=(n-4)-4$

$n_{48}=n_{47}-4=n_2-47\times 4$

$n_{48}=n,-188$

$n_{48}=1.5n_{48}-168$ $\therefore n_1=1.5n_{48}$

$\therefore n_{48}=376$

$n_1=1.5n_{48}=1.5\times 376=564$

$n_{42}=n_{41}-4=n_1+n\times 41$

$\therefore n_{42}=n_1-160=564-764$

$n_{4}2=400Hz$