Two cars P and Q are traveling along a motorway in the same direction. The leading car P travels at a steady speed of 12 m s⁻¹, the other car Q, traveling at a steady speed of 20 m s⁻¹, sound its horn to emit a steady note which P's driver estimates has a frequency of 830 Hz. What frequency does Q's own driver hear? (Speed of sound = 340 m s⁻¹) (Ans: 810 Hz)



Data Given:


Speed of car P (observer) = 12 m s⁻¹

Speed of car Q (source) = 20 m s⁻¹

As both cars are moving in the same direction So,

Relative Speed = `\v_s` = 20 m s⁻¹ - 12 m s⁻¹ = 8 m s⁻¹

Frequency Observed by P's driver = f ' = 830 Hz

Speed of sound = v = 340 m s⁻¹


To Find:


Frequency of Source (car Q)  = f  = ?


Solution:


As both the cars P and Q are traveling in relative motion in the same direction so using the general relation for finding the apparent frequency observed by the observer (i.e car P's divers):

f '  = `\frac {v}{v - v_s}` f

or

f = `\frac {v - v_s}{v}` f '

by putting values


f = `\frac {340 m s⁻¹ - 8 m s⁻¹}{340 m s⁻¹}` ｘ830 Hz

f = `\frac {332 m s⁻¹}{340 m s⁻¹}` ｘ830 Hz

f = 0.977 ｘ830 Hz

f = 810.470 Hz

or

f = 810 Hz ------------Ans

Hence the frequency of the source (car Q) was 810 Hz.


Similar Questions:

A sound source vibrates at 200 Hz and is receding from a stationary observer at 18 ms⁻¹. If the speed of sound is 331 ms⁻¹ then what frequency does the observer hear? (189.68Hz) 


A train sounds its horn before it sets off from the station and an observer waiting on the platform estimates its frequency at 1200 Hz. The trains then moves off and accelerates steadily. Fifty seconds after departure, the driver sounds the horn again and the platform observer estimates the frequency of 1140 Hz. Calculate the train speed 50 s after departure. How far from the station is the train after 50 s? (Speed of sound = 340 m s⁻¹). (Ans: 17.9 m s⁻¹, 448 m)




************************************

Shortcut Links For 


1. Website for School and College Level Physics   
2. Website for School and College Level Mathematics  
3. Website for Single National Curriculum Pakistan - All Subjects Notes 

© 2022-Onwards by Academic Skills and Knowledge (ASK)     

Note:  Write me in the comment box below for any query and also Share this information with your class-fellows and friends.