A driver in a car, approaching a vertical wall notices that the frequency of his car horn, has changed from $440\, Hz$ to $480 \,Hz ,$ when it gets reflected from the wall. If the speed of sound in air is $345 \,m / s ,$ then the speed of the car is $.......km/hr$
JEE MAIN 2020, Diffcult
Download our app for free and get started
$f _{1}=$ frequency heard by wall $= f _{ s }=\left(\frac{ v _{ s }}{ v _{ s }- v _{ c }}\right)$
$f _{2}=$ frequency heard by driver after reflection from wall
$f_{2}=\left(\frac{v_{s}+v_{c}}{v_{s}}\right) f_{1}=\left(\frac{v_{s}+v_{c}}{v_{s}-v_{c}}\right) f_{0}$
$\frac{f_{2}}{f_{0}}=\frac{v_{s}-v_{c}}{v_{s}+v_{c}}$
$\frac{48}{44}=\frac{v_{s}-v_{c}}{v_{s}+v_{c}}$
$12\left( v _{ s }+ v _{ c }\right)=11\left( v _{ s }- v _{ c }\right)$
$23 v _{ c }= v _{ s }$
$v _{ c }=\frac{ v _{ s }}{23}=\frac{345}{23}=15 m / s$
$=\frac{15 \times 18}{5}=54 km / hr$
Download our appand get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Similar Questions
- 1If two tuning forks $A$ and $B$ are sounded together, they produce $4$ beats per second. $A$ is then slightly loaded with wax, they produce $2$ beats when sounded again. The frequency of $A$ is $256.$ The frequency of $B$ will beView Solution
- 2A source of sound emits $200\pi W$ power which is uniformly distributed over a sphere of $10 m$ radius. What is the loudness of sound on the surface of a sphereView Solution
- 3Two adjacent piano keys are struck simultaneously. The notes emitted by them have frequencies ${n_1}$ and ${n_2}$. The number of beats heard per second isView Solution
- 4In a sonometer wire, the tension is maintained by suspending a $50.7 kg$ mass from the free end of the wire. The suspended mass has a volume of $ 0.0075 \, m^3$. The fundamental frequency of the wire is $260 Hz$. If the suspended mass is completely submerged in water, the fundamental frequency will become .... $Hz$ (take $g = 10 ms^{-2}$)View Solution
- 5A stretched string of length $l,$ fixed at both ends can sustain stationary waves of wavelength $\lambda ,$ given byView Solution
- 6A signal of $0.1\, kW$ is transmitted in a cable. The attenuation of cable is $-5 \,dB$ per $km$ and cable length is $20\, km$. The power received at receiver is $10^{-x} \, W$. The value of $x$ is ....... .View Solution
$\left[\right.$ Gain in $\left. dB =10 \log _{10}\left(\frac{ P _{0}}{ P _{i}}\right)\right]$
- 7Speed of sound in mercury at a certain temperature is $1450 \,m/s$. Given the density of mercury as $13.6 × 10^3 kg / m^3$, the bulk modulus for mercury isView Solution
- 8The rope shown at an instant is carrying a wave travelling towards right, created by a source vibrating at a frequency $n$. Consider the following statementsView Solution
$I.$ The speed of the wave is $4n \times ab$
$II.$ The medium at $a$ will be in the same phase as $d$ after $\frac{4}{{3n}}s$
$III.$ The phase difference between $b$ and $e$ is $\frac{{3\pi }}{2}$
Which of these statements are correct
- 9View SolutionIn stationary waves all particles between two nodes pass through the mean position
- 10A string fixed at both ends is in resonance in its $2^{nd}$ harmonic with a tuning fork of frequency $f_1$. Now its one end becomes free. If the frequency of the tuning fork is increased slowly from $f_1$ then again a resonance is obtained when the frequency is $f_2$. If in this case the string vibrates in $n^{th}$ harmonic thenView Solution