A man is watching two trains,one leaving and | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Let $n = 240\,Hz$ be the frequency of the whistles,$v_s = 4\,m/s$ be the speed of the trains,and $v = 320\,m/s$ be the speed of sound.The apparent

Vedclass · Accepted Answer

$6$

Vedclass · Answer

(D) Let $n = 240\,Hz$ be the frequency of the whistles,$v_s = 4\,m/s$ be the speed of the trains,and $v = 320\,m/s$ be the speed of sound.The apparent frequency $n'$ heard from the train approaching the observer is given by the Doppler effect formula:$n' = n \left[ \frac{v}{v - v_s} ight]$The apparent frequency $n''$ heard from the train moving away from the observer is given by:$n'' = n \left[ \frac{v}{v + v_s} ight]$The number of beats per second is the difference between these two frequencies:$\Delta n = n' - n'' = n \left[ \frac{v}{v - v_s} - \frac{v}{v + v_s} ight]$$\Delta n = nv \left[ \frac{(v + v_s) - (v - v_s)}{v^2 - v_s^2} ight] = nv \left[ \frac{2v_s}{v^2 - v_s^2} ight]$Since $v_s$ is very small compared to $v$,we can approximate $v^2 - v_s^2 \approx v^2$:$\Delta n \approx nv \left[ \frac{2v_s}{v^2} ight] = \frac{2nv_s}{v}$Substituting the values:$\Delta n = \frac{2 	imes 240 	imes 4}{320} = \frac{1920}{320} = 6\,Hz$Thus,the number of beats per second heard by the man is $6$.

$A$ man is watching two trains,one leaving and the other coming with equal speed of $4\,m/s$. If they sound their whistles each of frequency $240\,Hz$,the number of beats per second heard by the man will be equal to (velocity of sound in air $= 320\,m/s$)

Similar Questions

$A$ metal $M$ readily forms its sulphate $MSO_4$,which is water soluble. It forms oxide $MO$ which becomes inert on heating. It forms insoluble hydroxide which is soluble in $NaOH$. The metal $M$ is

The population $p(t)$ at time $t$ of a certain mouse species follows the differential equation $\frac{d p(t)}{d t}=0.5 p(t)-450$. If $p(0)=850$, then the time at which the population becomes zero is

$\frac{\tan 80^{\circ}-\tan 10^{\circ}}{\tan 70^{\circ}}$ is equal to

The angle between the lines $2x = 3y = -z$ and $6x = -y = -4z$ is ......... $^o$.

Which of the following is a $C_4$ plant?

Vedclass Test Series

Exam Paper Generator

Online Exam Module