A rocket is moving at a speed of $ 200 \,m/s $ towards a stationary target. While moving it emits a wave of frequency $ 1000 \,Hz $ . Some of the sound reaching the target gets reflected back to the rocket as an echo. The frequency of the echo as detected by the rocket is (velocity of sound $ = 330 \,m/s $ )
Given, speed of rocket, $v_{1}=200 \, m/s$ Frequency emitted by the rocket, $v_{1}=1000\,HZ$ Velocity of sound, $v_{sound}=330\, m/s$
Apply Doppler's effect in sound's equation $v=\frac{v+u_{0}}{v-u_{1}}$ Putting values, $v_{1}=\frac{330+0}{330-220} \times 1000$ $v_{1}=\frac{33}{13} \times 1000\,Hz \dots(i)$ This frequency is reflected back to the rocket
Apply Doppler's effect in sound's equation $v_{2}=\frac{330+200}{300}v_{1}$ $=\frac{530}{330}\times \frac{33}{13}\times 1000$ [from E (i)] $=\frac{53}{13}\times1000=4076.92\,Hz$ Thus, the most appropriate option is (d)
Waves are a disturbance through which the energy travels from one point to another. Most acquainted are surface waves that tour on the water, but sound, mild, and the movement of subatomic particles all exhibit wavelike properties. inside the most effective waves, the disturbance oscillates periodically (see periodic movement) with a set frequency and wavelength.
Types of Waves:
Transverse Waves -
Waves in which the medium moves at right angles to the direction of the wave.
Examples of transverse waves:
Water waves (ripples of gravity waves, not sound through water)
Light waves
S-wave earthquake waves
Stringed instruments
Torsion wave
The high point of a transverse wave is a crest. The low part is a trough.
Longitudinal Wave -
A longitudinal wave has the movement of the particles in the medium in the same dimension as the direction of movement of the wave.
