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# Solution for 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 360 Km H–1. What is the Frequency of Sound Reflected by the Submarine? Take the Speed of Sound in Water to Be 1450 - CBSE (Science) Class 11 - Physics

ConceptThe Speed of a Travelling Wave

#### 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 360 km h–1. What is the frequency of sound reflected by the submarine? Take the speed of sound in water to be 1450 m s–1.

#### Solution 1

Her frequency of Sonar (source) = 40.0 kHz = 40xx10^3 "Hz"

Speed of sound waves, v= 1450 ms^(-1)

Speed of observers, v_0 = 360 "km/h" = 360 xx  5/18 = 100 ms^(-1)

Since the source is at rest and obsever moves toward the source (SONAR)

:. v' = (v+v_0)/v.v = (1450+100)/1450 xx 40xx 10^3 = 4.276 xx 10^(4) Hz

This frequency (v') is reflected by the enemy ship and is observed by the SONAR (which now act as observer). Therefore, in this case v_s = 360 km/h = 100 ms^(-1)

:. Apparent frequency, v" = v/(v - v_s) v' = 1450/(1450 - 100) xx 4.276 xx 10^4

= 4.59 xx 10^4 Hz = 45.9 kHz

#### Solution 2

Operating frequency of the SONAR system, ν = 40 kHz

Speed of the enemy submarine, ve = 360 km/h = 100 m/s

Speed of sound in water, = 1450 m/s

The source is at rest and the observer (enemy submarine) is moving toward it. Hence, the apparent frequency (V') received and reflected by the submarine is given by the relation:

v' = ((v+v_e)/v) v

= ((1450+100)/1450) xx 40 = 42.76 kHz

The frequency (v") received by the enemy submarine is given by the relation:

v" = (v/(v+v_s))v'

where v_s = 100 "m/s"

:. v" = (1450/(1450 - 100))xx 42.76 = 45.93  kHz

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#### APPEARS IN

Solution 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 360 Km H–1. What is the Frequency of Sound Reflected by the Submarine? Take the Speed of Sound in Water to Be 1450 Concept: The Speed of a Travelling Wave.
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