The apparent frequency of a note, when a listener moves towards a stationary source, with velocity of $40 m/s$ is $200 Hz$. When he moves away from the same source with the same speed, the apparent frequency of the same note is $160 Hz$. The velocity of sound in air is (in $m/s$)
Medium
Download our app for free and get started
(a) When a listener moves towards a stationary source apparent frequency
$n' = \left( {\frac{{v + {v_0}}}{v}} \right)\,$$n = 200$…..$(i)$
When listener moves away from the same source
$n'' = \frac{{(v - {v_O})}}{v}n = 160$…..$(ii)$
From $(i)$ and $(ii)$
$\frac{{v + {v_O}}}{{v - {v_O}}} = \frac{{200}}{{160}}$
$n' = \left( {\frac{{v + {v_0}}}{v}} \right)\,$$n = 200$…..$(i)$
When listener moves away from the same source
$n'' = \frac{{(v - {v_O})}}{v}n = 160$…..$(ii)$
From $(i)$ and $(ii)$
$\frac{{v + {v_O}}}{{v - {v_O}}} = \frac{{200}}{{160}}$
==> $\frac{{v + {v_O}}}{{v - {v_O}}} = \frac{5}{4}$
==> $v = 360m/\sec $
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
- 1A steel rod $100 \,cm$ long is clamped at its middle. The fundamental frequency of longitudinal vibrations of the rod are given to be $2.53\,kHz$. What is the speed of sound in steel ..... $km/sec$View Solution
- 2A mass of $20\ kg$ is hanging with support of two strings of same linear mass density. Now pulses are generated in both strings at same time near the joint at mass. Ratio of time, taken by a pulse travel through string $1$ to that taken by pulse on string $2$ isView Solution
- 3Two waves of lengths $50 \;cm$ and $51\; cm$ produced $12$ beats per second. The velocity of sound is .... $m/s$View Solution
- 4A person standing at a distance of $6\,\, m$ from a source of sound receives sound wave in two ways, one directly from the source and other after reflection from a rigid boundary as shown in the figure. The maximum wavelength for which, the person will receive maximum sound intensity, is .... $m$View Solution
- 5A string is producing transverse vibration whose equation is $y = 0.021\;\sin (x + 30t)$, Where $x$ and $y$ are in meters and $t$ is in seconds. If the linear density of the string is $1.3 \times {10^{ - 4}}\,kg/m,$ then the tension in the string in $N$ will beView Solution
- 6For a particular resonance tube, following are four of the six harmonics below $1000 Hz$; $300,600,750$ and $900 \,Hz$. The two missing harmonics areView Solution
- 7Two waves of frequencies $20 Hz$ and $30 Hz.$ Travels out from a common point. The phase difference between them after $0.6 sec$ isView Solution
- 8On a long horizontally moving belt, a child runs to and fro with a speed $9\, km\, h^{-1}$ (with respect to the belt) between his father and mother located $50\, m$ apart on the moving belt. The belt moves with a speed of $4\, km\, h^{-1}$. For an observer on a stationary platform, the speed of the child running in the direction of motion of the belt is ..... $km\,h^{-1}$View Solution
- 9The source producing sound and an observer both are moving along the direction of propagation of sound waves. If the respective velocities of sound, source and an observer are $v, {v_s}$ and ${v_o}$, then the apparent frequency heard by the observer will be ($n =$ frequency of sound)View Solution
- 10Three waves of equal frequency having amplitudes $10\mu m,$ $4\mu m,$ $7\mu m$ arrive at a given point with successive phase difference of $\frac{\pi }{2},$ the amplitude of the resulting wave in $\mu m$ is given byView Solution