# **Sonar for Class 5 Maths**

Sonar is a machine which is used for underwater sound waves. Here students will learn about what sonar is, the types of sonar, the application of sonar, and the working of sonar that also connect with the mathematical concept of time, speed, and distance.

## What Is Sonar?

The word **SONAR** stands for “Sound Navigation and Ranging”.

It is the direct application of the principle of reflection of sound.

SONAR is permanently fastened to ships or submarines to easily calculate the ocean’s depth.

It consists of two parts:

- Transmitter
- Receiver (Detector)

## What Are Types of Sonar:

- Active Sonar
- Passive Sonar

## What Is Active Sonar:

An active sonar consists of both the parts, transmitters, and receiver. In this, the system emits the sounds, and the receiver hears the echoes and detects them.

## What is Passive Sonar:

A passive sonar consists only of the receiver. In this, the receiver listens to the sound waves generated by the surrounding objects.

## Explain the Working and Application of Sonar:

**Explain the Working of Sonar:**

The transmitter continuously produces ultrasonic waves and send it into the ocean. The velocity of the ultrasonic waves in water is V.

Suppose that some obstacle is present at the ocean's depth “d”. The waves of the transmitter travel the distance “d” and get reflected toward the ship in the same angel and velocity.

The Receiver receives the reflected waves and observes the time between transmitting them and receiving them after reflection.

The formula calculates the depth of the ocean

d = were,

V = Velocity of the waves

t = Time interval between the transmission and the reception.

**Application of Sonar:**

- It is used to detect the presence of obstacles, such as rocks.
- It is used to detect hidden submarines, which helps to determine the location of the enemy forces.
- The Ocean’s depth can be easily calculated using Sonar.

### Example:

A navy officer sends ultrasonic waves from a ship that are returned from the seabed and detected after 4 seconds. Suppose the speed of the ultrasound through the seawater is 1564 m /sec. What is the seabed distance from the ship?

### Solution:

The speed of the ultrasound (V) = 1546 m/sec

The time taken (t) = 4 sec

The formula to calculate the distance is d = Vt2.

Substitute 1546 for V and 4 for t in the formula and then simplify to get the distance.

Therefore, the distance of the seabed from the ship was 3128 m.

**Time, Speed and Distance Question:**

## Question 1:

In a SONAR, Ultrasonic Waves Are Sent Into the Seawater, and the Reflected Waves From the Sunken Ship Are Received After 1.5 Sec. If the Waves’ Velocity in the Seawater Is 1450 m/Sec. Find the Depth of the Sunken Ship.

### Solution:

The speed of the ultrasound (V) = 1450 m/sec

The time taken (t) = 1.5 sec

The formula to calculate the distance is d = Vt2.

Substitute 1450 for V and 1.5 for t in the formula and then simplify to get the distance.

Therefore, the depth of the sunken ship was 1087.50 m.

## Question 2:

The Navy Officer Found That in a Submarine Equipped With Sonar, the Time Delay Between the Generation of the Pulse and Its Echo After Reflection From an Enemy Submarine Is Observed to Be 0.02 Hours. Calculate the Distance of the Enemy Submarine in Kilometres if the Speed of the Ultrasound Is 1400 m/Sec.

### Solution:

### Step 1:

The time taken (t) = 0.01 hours.

We know that 1 hour = 3600 seconds.

Multiply 0.02 hours by 3600 to convert 0.02 hours to equivalent seconds.

0.02 × 3600 = 72

### Step 2:

The speed of the ultrasound (V) = 1400 m/sec.

Time taken (t) = 72 sec.

The formula to calculate the distance is d = Vt2.

Substitute 1400 for V and 72 for t in the procedure and then simplify to get the space.

d =

Therefore, the distance of the enemy submarine is 50,400 m.

### Step 3:

We know that 1 km = 1000 m

Divide 50,400 by 1000 to convert 50,400 m to kilometres.

50,400 ÷ 1000 = 50.4

Therefore, the distance of the enemy submarine is 50.4 km.

## Question 3:

A Ship on the Surface of t he Water Sends a Signal and Receives It Back From a Submarine Inside the Water. If the Speed of the Sound in the Water Is 1450 m/Sec and the Submarine Distance From the Ship Equals 2.9 km. Find the Time It Took to Receive the Signal.

### Solution:

### Step 1:

The speed of the ultrasound (V) = 1450 m/sec

Distance (d) = 2.9 km

We know 1 km = 1000 m

Multiply 2.9 by 1000 to convert 2.9 km to equivalent meters.

2.9 × 1000 = 2900 m

### Step 2:

From the formula of SONAR, we have

d =It follows that

t =Substitute 1450 for V and 2900 for d in the formula and then simplify to get time.

t =Therefore, it must have taken 4 sec to receive the signal.

## Question 4:

Sonar Was Used to Calculate the Distance of the Marine Mammal From the Ship. It Was Measured That the Mammal Was at a Distance of 54,30,000 cm. The Time Between the Transmitter and the Receiver of the Waves Was 5 Minutes. Calculate the Spend of the Waves in the Sound.

### Solution:

### Step 1:

Distance = 54,30,000 cm

We know 1 m = 100 cm

Divide 54,30,000 by 100 to convert 54,30,000 cm to equivalent meters.

54,30,000 ÷ 100 = 54,300 m

### Step 2:

We know that 1 minute = 60 seconds.

Multiply five by 60 to convert 15 minutes to a second.

5 × 60 = 300

### Step 3:

From the formula of SONAR, we have

d =It follows that

V =Substitute 54,300 for d and 300 for t in the formula and then simplify to get the speed.

V =Therefore, the sound travels at the speed of 362 m/sec.