# Sonar and Sound Speed Calculation Quiz

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## 3 Questions

### Calculate the distance of the enemy submarine given the time delay between the generation of a pulse and its echo is 80 s, and the speed of sound in water is 1460 m/s.

Let the distance be represented by d. The total time taken to receive the sound signal (forward + backward) is 2t. Given 2t = 80, the velocity of sound in water is 1460 m/s. Using the formula distance = velocity * time, we have d = 1460 * 80 / 2 = 58400 m.

### Calculate the area of the circle with a radius of 3.12 m, rounding off to three significant figures.

Given that the radius of the circle is 3.12 m, we have r = 3.12 m. The area of the circle is calculated using the formula A = πr^2, where A = π * (3.12)^2 = 30.59 m^2. Rounding off to three significant figures, the area is 30.6 m^2.

### Prove the dependence of the frequency of a vibrating string on the applied force (F), length (l), and mass per unit length (m).

The frequency (f) of a vibrating string is given by the equation f = (1/2l) * sqrt(F / m), where l is the length, F is the applied force, and m is the mass per unit length. This equation demonstrates the dependence of the frequency on the applied force, length, and mass per unit length.

## Study Notes

### Distance of Enemy Submarine

• Time delay between pulse generation and its echo is 80 s
• Speed of sound in water is 1460 m/s
• Distance of enemy submarine can be calculated using the formula: Distance = Speed x Time = 1460 m/s x 80 s

### Area of Circle

• Radius of circle is 3.12 m
• Area of circle formula: A = πr^2
• Area of circle ≈ 3.14 x (3.12 m)^2 ≈ 30.5 m^2 (rounded to three significant figures)

### Vibrating String Frequency

• Frequency of a vibrating string depends on applied force (F), length (l), and mass per unit length (m)
• Mathematical relationship: f ∝ √(F/lm)
• Increasing the applied force, decreasing the length, or decreasing the mass per unit length increases the frequency of the vibrating string

Test your numerical problem-solving skills with this quiz. Solve practical problems involving sonar, sound speed in water, and distance calculations.

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