Dolphins can hear ultrasound with frequencies up to 280 kHz. What is the speed of sound in water if the wavelength of ultrasound with a frequency of 2.80 × 10^5 Hz is 0.510 cm?
How long would it take this sound wave to travel to a dolphin 3.00 km away?
a. L = V/F = 5.1*10^-3.
V/(2.8*10^5) = 5.1*10^-3.
V = m/s.
b. d = V*t; t = d/V = 3000/V.
To find the speed of sound in water, we can use the equation:
Speed of sound = Frequency x Wavelength
Given:
- Frequency = 2.80 × 10^5 Hz
- Wavelength = 0.510 cm (or 0.00510 m)
Speed of sound = (2.80 × 10^5 Hz) x (0.00510 m)
= 1430 m/s
Therefore, the speed of sound in water is 1430 m/s.
To calculate the time it would take for the sound wave to travel to a dolphin 3.00 km away, we use the formula:
Time = Distance / Speed
Given:
- Distance = 3.00 km (or 3000 m)
- Speed = 1430 m/s
Time = 3000 m / 1430 m/s
= 2.0986 seconds (rounded to 4 decimal places)
Therefore, it would take approximately 2.0986 seconds for the sound wave to travel to a dolphin 3.00 km away.
To calculate the speed of sound in water, we can use the formula:
Speed of sound = Frequency × Wavelength
Given that the frequency is 2.80 × 10^5 Hz and the wavelength is 0.510 cm, we can substitute these values into the formula:
Speed of sound = 2.80 × 10^5 Hz × 0.510 cm
Now, we need to convert the wavelength from centimeters to meters since the speed of sound is usually given in meters per second:
Speed of sound = 2.80 × 10^5 Hz × (0.510 cm / 100 cm/ m)
Simplifying the expression:
Speed of sound = 2.80 × 10^5 Hz × 0.00510 m
Calculating the value:
Speed of sound = 1428 m/s
So, the speed of sound in water is approximately 1428 meters per second.
Now, let's find out how long it would take the sound wave to travel to a dolphin 3.00 km away.
To do this, we can use the formula:
Time = Distance / Speed
Given that the distance is 3.00 km and the speed of sound is 1428 m/s, we need to convert the distance to meters for consistency:
Distance = 3.00 km × (1000 m / 1 km)
Substituting the values into the formula:
Time = (3.00 km × 1000 m) / 1428 m/s
Simplifying the expression:
Time = 3000 m / 1428 m/s
Calculating the value:
Time = 2.10 seconds
Therefore, it would take approximately 2.10 seconds for the sound wave to travel to a dolphin 3.00 km away.