Two cars $A$ and $B$ are moving in the same direction with speeds $36\, km/hr$ and $54 \,km/hr$ respectively. Car $B$ is ahead of $A$. If $A$ sounds horn of frequency  $1000\, Hz$ and the speed of sound in air is $340\, m/s$, the frequency of sound  received by the driver of car $B$ is ….. $Hz$

A train approaching a railway plateform with a speed of  $20\,\,m\,s^{-1}$ starts blowing the whistle speed of sound in air is $340\,\,ms^{-1}.$ If frequency of the emitted sound from the whistle is  $640\,\,Hz,$  the frequency of sound as heard by person standing on the platform is …. $Hz$

A string fixed at one end is vibrating in its second overtone. The length of the string is $10\  cm$ and maximum amplitude of vibration of particles of the string is $2\ mm$ . Then the amplitude of the particle at $9\ cm$ from the open end is

Fundamental frequency of sonometer wire is $n$. If the length, tension and diameter of wire are tripled, the new fundamental frequency is

Two tuning forks having frequency $256\, Hz \,(A)$ and $262\, Hz \,(B)$ tuning fork. $A$ produces some beats per second with unknown tuning fork, same unknown tuning fork  produce double beats per second from $B$ tuning fork then the frequency of unknown tuning fork is :- ………… $\mathrm{Hz}$