Question

A ship at sea sounds a whistle blast, and an echo returns from the coastal land 22.0 s later. How many km is it to the coastal land if the air temperature is 16.8°C?

Answer 1

Using the speed of sound at 16.8°C and the echo return time, the distance to the coastal land is approximately 3.756 km.

Step-by-step explanation:

To calculate the distance to the coastal land, we need to use the speed of sound in air, which depends on the air temperature. The formula for the speed of sound in air at a given temperature in degrees Celsius is v = 331.4 + 0.6T m/s, where T is the air temperature. At 16.8°C, the speed of sound is v = 331.4 + 0.6(16.8) = 341.48 m/s. The total travel time for the sound wave is 22.0 s, which includes the trip to the coastal land and back. Therefore, the one-way travel time is 22.0 s / 2 = 11.0 s.

Using the formula distance = speed × time, the distance to the coastal land is 341.48 m/s × 11.0 s = 3756.28 m or approximately 3.756 km.

Answer 2

Answer: 3752 m

Step-by-step explanation:

The speed of sound in the air, at
`0 \°C` is
`331.5 m/s`, and for each degree Celsius the temperature rises, the speed of the sound increases by
`0.6 m/s`. So, if we estimate the speed of sound at
`16 \°C` it will be
`341.1 m/s`.

On the other hand, the speed of sound
`V` is defined as the distance traveled
`d` in a especific time
`t`:

`V=(d)/(t)`

Where:

`V=341.1 m/s` is the speed of sound

`t=(22 s)/(2)=11 s` is half the time the sound wave travels from the ship and then returns from the coastal land

`d` is the distance between the ship and the coastal land

`341.1 m/s=(d)/(11 s)`

Finding
`d`:

`d=(341.1 m/s)(11 s)`

Finally:

`d=3752.1 m`