A column of air and a tuning fork produce 4 beats per second when sounded together. The tuning fork gives the lower note. The temperature of air is `15^(@)C`. When the temperature falls to `10^(@)C`, the two produce 3 beats per second. Find the frequency of the fork.

Options

A. 210 Hz
B. 113 Hz
C. 112 Hz
D. 110 Hz

Answer

D

Explanation

Let the frequency of the tuning fork be n Hz
Then frequency of air column at `15^@C=n+4`
Frequency of air column at `10^@C=n+3`
`v_15=(n+14)lamda and v_10=(n+3) lamda`
`therefore v_15/v_10=(n+4)/(n+3)`
the speed of sound is directly proportional to the square root to the absolute temperature
`thereforev_15/v_10=sqrt((15+273)/(10+273))=sqrt288/283`
`therefore (n+4)/(n+3)=sqrt288/283=(1+5/283)^(1//2)`
`implies1+1/(n+3)=1+1//2 times5/283=1+5/566`
`implies1/(n+3)=5/566 impliesn+3=113 implies n=110 Hz`