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Waves — Physics STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 SciencePhysicsWaves3 Marks
Question
A SONAR system fixed in a submarine operates at a frequency 40.0 kHz. An enemy submarine moves towards the SONAR with a speed of 360km h–1. What is the frequency of sound reflected by the submarine? Take the speed of sound in water to be 1450m s–1.
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Answer

The frequency of SONAR received by enemy submarine will be further reflected back to SONAR which it will receive again with a different frequency.
SONAR frequency(Vs) = 40kHz = 40 × 103Hz
Speed of enemy submarine(Vo) = 360km/h
$=360\times\frac{5}{18}=100\text{m/s}$
Speed of sound in water = 1450m/s
Apparent frequency received by submarine is
$\text{f}'=\Big\{\frac{\text{V}+\text{V}_\text{o}}{\text{V}}\Big\}\text{f}=\Big\{\frac{1450+100}{1450}\Big\}\times40=42.76\text{kHz}$
Now, the reflected wave have a different frequency,
$\text{f}"=\Big\{\frac{\text{V}}{\text{V}-\text{V}_\text{o}}\Big\}\text{f}'=\Big\{\frac{1450}{1450-100}\Big\}\times42.76=45.93\text{kHz}$

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