Question

A tuning fork and an air column whose temperature is ${51}^{\circ }C$ produce 4 beats in one second, when sounded together. When the temperature of air column decreases the number of beats per second decreases. When the temperature remains ${160}^{\circ }C$ only one beat per second is produced. The frequency of the tuning fork is

Answer 1

When temp. decreases, speed of sound in air decreases, since no. of beats per second is less at lower tempertaure we coclude that frequency of aircolumn is higher than freq. of tuning fork.

let v be freq. of tuning fork, then at 51 degrees frq. of air column will be (n+4) where n is freq. of tuning fork

at 16 degrees , frewq. of air column will be (n+1)

v51/v16 = (n+4)*k / (n+1)*k

(n+4)/(n+1) = (273+51)1/2 / (273+16)1/2

on solving ofr n , we'll get n = 50 Hz