Question 12: Waves

Question

A submarine A travelling at 17 m/s is being chased along the line of its velocity by another submarine B travelling at 34 m/s. B sends a sonar signal of 600 Hz to detect A and receives a reflected sound of frequency $$
u$$. The of $$
u$$ is
[Speed of sound in water = 1500 ms$$-$$1]

Accepted Answer

Given, velocity of submarine A, v
A
= 17 m/s
Velocity of submarine B, v
B
= 34 m/s
Signal sent by submarine B is detected by submarine A can be shown as
Frequency of signal, f
0
= 600 Hz
Speed of sound in water v
s
= 1500 ms
$$-$$1
Frequency received by submarine A is
$${f_1} = \left( {{{{v_s} - {v_A}} \over {{v_s} - {v_B}}}} ight){f_0} = \left[ {{{1500 - 17} \over {1500 - 34}}} ight] 	imes 600$$ Hz
$${f_1} = {{1483} \over {1466}} 	imes 600$$ ..... (i)
Frequency received by submarine B is
$${f_2} = \left( {{{{v_s} + {v_B}} \over {{v_s} + {v_A}}}} ight){f_1}$$
Substituting given values and f
1
value from Eq. (i), we get
$${f_2} = \left( {{{1500 + 34} \over {1500 + 17}}} ight) 	imes \left[ {{{1483} \over {1466}} 	imes 600} ight]$$
$${f_2} = 1.0112 	imes 1.0115 	imes 600$$
$${f_2} = 613.7$$ Hz.

Answer

613.7 Hz

Answer

6137 Hz

Answer

62 Hz

Answer

539 Hz

Waves

A submarine A travelling at 17 m/s is being chased along the line of its velocity by another submarine B travelling at 34 m/s. B sends a sonar signal of 600 Hz to detect A and receives a reflected sound of frequency $\nu. The of \nu is [Speed of sound in water = 1500 ms-$1]

Choose the correct answer: