$A$ tuning fork of frequency $280\, Hz$ produces $10$ beats per second when sounded with a vibrating sonometer string. When the tension in the string increases slightly,it produces $11$ beats per second. The original frequency of the vibrating sonometer string is ... $Hz$.

Two vibrating tuning forks produce progressive waves given by $y_1 = 4 \sin(500 \pi t)$ and $y_2 = 2 \sin(506 \pi t)$. These tuning forks are held near the ear of a person. The person will hear

Two tuning forks have frequencies $380 \ Hz$ and $384 \ Hz$ respectively. When they are sounded together,they produce $4$ beats per second. After hearing the maximum sound,how long will it take to hear the minimum sound in seconds?

When two tuning forks (fork $1$ and fork $2$) are sounded simultaneously,$4$ beats per second are heard. Now,some tape is attached to the prong of fork $2$. When the tuning forks are sounded again,$6$ beats per second are heard. If the frequency of fork $1$ is $200 \, Hz$,then what was the original frequency of fork $2$ (in $, Hz$)?

Two sitar strings $A$ and $B$ playing the note $Sa$ are slightly out of tune and produce beats of frequency $5 \ Hz$. The tension of the string $B$ is slightly decreased and the beat frequency is found to decrease to $3 \ Hz$. What is the original frequency of $B$,if the frequency of $A$ is $255 \ Hz$?

$41$ tuning forks are arranged in increasing order of frequency such that each produces $5 \text{ beats/second}$ with the next tuning fork. If the frequency of the last tuning fork is double that of the frequency of the first fork,then the frequency of the first and last fork is: