$A$ bus is moving with a velocity of $5 \,m/s$ towards a wall. The driver blows the horn of frequency $165 \,Hz$. If the speed of sound in air is $335 \,m/s$, then after reflection of sound wave, the number of beats per second heard by the passengers in the bus will be

$A$ stationary tuning fork is in resonance with an air column in a pipe. If the tuning fork is moved with a speed of $2 \ m/s$ in front of the open end of the pipe and parallel to it,the length of the pipe should be changed for the resonance to occur with the moving tuning fork. If the speed of sound in air is $320 \ m/s$,the smallest value of the percentage change required in the length of the pipe is. . . . . .

$A$ source,approaching with speed $u$ towards the open end of a stationary pipe of length $L$,is emitting a sound of frequency $f_s$. The farther end of the pipe is closed. The speed of sound in air is $v$ and $f_0$ is the fundamental frequency of the pipe. For which of the following combination$(s)$ of $u$ and $f_s$,will the sound reaching the pipe lead to a resonance?
$(A)$ $u=0.8 v$ and $f_s=f_0$
$(B)$ $u=0.8 v$ and $f_s=2 f_0$
$(C)$ $u=0.8 v$ and $f_s=0.5 f_0$
$(D)$ $u=0.5 v$ and $f_s=1.5 f_0$

When the observer moves towards a stationary source with velocity $V_1$, the apparent frequency of the emitted note is $F_1$. When the observer moves away from the source with velocity $V_1$, the apparent frequency is $F_2$. If $V$ is the speed of sound in air and $F_1/F_2 = 2$, then $V/V_1 =$

$A$ train $S_1$,moving with a uniform velocity of $108 \ km/h$,approaches another train $S_2$ standing on a platform. An observer $O$ moves with a uniform velocity of $36 \ km/h$ towards $S_2$,as shown in the figure. Both the trains are blowing whistles of the same frequency $120 \ Hz$. When $O$ is $600 \ m$ away from $S_2$ and the distance between $S_1$ and $S_2$ is $800 \ m$,the number of beats heard by $O$ is: [Speed of sound $= 330 \ m/s$]

$A$ stationary sound source $S$ of frequency $334 \, Hz$ and a stationary observer $O$ are placed near a reflecting surface moving away from the source with velocity $u = 2 \, m/s$ as shown in the figure. If the velocity of the sound waves in air is $V = 330 \, m/s$,the apparent frequency of the echo heard by the observer is ... $Hz$.