A motorcyclist is moving around a circular tr | vedclass

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

Question

(D) The Doppler effect formula for a moving observer and a stationary source is given by $n' = n \left( \frac{v \pm v_o}{v} \right)$,where $v$ is the

Vedclass · Accepted Answer

$573$

Vedclass · Answer

(D) The Doppler effect formula for a moving observer and a stationary source is given by $n' = n \left( \frac{v \pm v_o}{v} ight)$,where $v$ is the speed of sound and $v_o$ is the component of the observer's velocity along the line joining the source and the observer.The actual frequency $n$ is heard when the apparent frequency $n' = n$,which occurs when the component of the observer's velocity along the line joining the source and the observer is zero. This happens when the velocity vector of the motorcyclist is perpendicular to the line joining the siren at $Y$ and the motorcyclist.In one complete circular revolution,there are $2$ such points where the velocity vector is perpendicular to the radial line connecting the center of the circle to the source (or more accurately,the line of sight from the source to the observer). Thus,the motorcyclist hears the actual frequency $2$ times per revolution.The time period of one revolution $T$ is given by $T = \frac{2 \pi R}{v_o} = \frac{2 \pi 	imes 50}{25} = 4 \pi \ s$.The number of revolutions in one hour $(3600 \ s)$ is $N = \frac{3600}{T} = \frac{3600}{4 \pi} = \frac{900}{\pi} \approx \frac{900}{3.14159} \approx 286.48$.Since the motorcyclist hears the actual frequency $2$ times per revolution,the total number of times in an hour is $2 	imes 286.48 \approx 572.96$,which is approximately $573$.

$A$ motorcyclist is moving around a circular track of radius $50 \ m$ with a constant speed of $25 \ m/s$. $A$ static siren at point $Y$ emits sound of frequency $n$. How many times (approximately) in an hour will the motorcyclist hear the sound of the actual frequency $n$?

Similar Questions

With what velocity should an observer approach a stationary sound source,so that the apparent frequency of sound appears double the actual frequency? (Let $v$ be the velocity of sound).

An observer is approaching with a speed $v$ towards a stationary source emitting sound waves of wavelength $\lambda_0$. The wavelength shift detected by the observer is (Take $c$ as the speed of sound).

An observer moves towards a stationary source of sound with a speed $\frac{1}{5}^{\text{th}}$ of the speed of sound. The wavelength and frequency of the waves emitted by the source are $\lambda$ and $f$ respectively. The apparent frequency and wavelength heard by the observer are respectively,

$A$ source of sound of frequency $450 \text{ cycles/sec}$ is moving towards a stationary observer with $34 \text{ m/sec}$ speed. If the speed of sound is $340 \text{ m/sec}$,then the apparent frequency will be ..... $\text{cycles/sec}$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module