Two vibrating tuning forks produce waves given by ${y_1} = 4\sin 500\pi t$ and ${y_2} = 2\sin 506\pi t.$  Number of beats produced per minute is

A tuning of fork of frequency $392\, Hz$, resonates with $50\, cm$ length of a string under tension $(T)$. If length of the string is decreased by $2\%$, keeping the tension constant, the number of beats heard when the string and the tuning fork made to vibrate simultaneously is

A set of $24$ tunning fork is arranged in a series of increasing frequencies. If each fork gives $4\, beats/second$ with the preceeding one and frequency of last tunning fork is two times of first fork. Find frequency of $5^{th}$ tunning fork  .... $Hz$

The length of open organ pipe is $L$ and fundamental frequency is $f$. Now it is immersed into water upto half of its length now the frequency of organ pipe will be

Fundamental frequency of a sonometer wire is $n$ . If the length and diameter of the wire are doubled keeping the tension same, then the new fundamental frequency is

A car $P$ approaching a crossing at a speed of $10\, m/s$ sounds a horn of frequency $700\, Hz$ when $40\, m$ in front of the crossing. Speed of sound in air is $340\, m/s$. Another car $Q$ is at rest on a road which is perpendicular to the road on which car $P$ is reaching the crossing (see figure). The driver of car $Q$ hears the sound of the horn of car $P$ when he is $30\, m$ in front of the crossing. The apparent frequency heard by the driver of car $Q$ is ...... $Hz$