The amplitude of a wave disturbance propagating in the positive $X-$ direction is given by $y = 1/(1 + x^2)$ at time $t = 0$ and by $y = 1/[1 + (x -1)^2]$ at $t = 2$ seconds, where $x$ and $y$ are in metres. The shape of the wave disturbance does not change during the propagation. The velocity of the wave is ..... $ms^{-1}$
$1$
$0.5$
$1.5$
$2$
A closed organ pipe has a frequency $'n'$. If its length is doubled and radius is halved, its frequency nearly becomes
A car blowing a horn of frequency $350\, Hz$ is moving normally towards a wall with a speed of $5 \,m/s$. The beat frequency heard by a person standing between the car and the wall is ..... $Hz$ (speed of sound in air $= 350\, m/s$)
A train is moving towards a stationary observer. Which of the following curve best represents the frequency received by observer $f$ as a function of time ?
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
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 .................. $\mathrm{Hz}$