The range of human hearing extends from approxmately 20 HZ to 20 000 HZ. Find the wavelenghts of these extremes when the speed of sound in air is equal to 343 m/s.
A dolphin is 25 degrees C sea water emits a sound directed toward the bottom of the ocean 150 m below. How much time passes before it hears an echo?
1. L = V*T = 343m/s * (1/20)s. = 17.2 m.
L = 343m/s * (1/20000)s. = 0.0172 m.
2. d = 2 * 150m = 300 m. = Tot. dist.
T = d/V = 300/343 = 0.88 s.
To find the wavelengths of the extremes of human hearing, we can use the formula:
Wavelength = Speed of Sound / Frequency
At the lower limit of human hearing, the frequency is 20 Hz. Plugging in the given speed of sound in air, which is 343 m/s, we can calculate the wavelength:
Wavelength (at 20 Hz) = 343 m/s / 20 Hz
Wavelength (at 20 Hz) = 17.15 meters
Similarly, at the upper limit of human hearing, the frequency is 20,000 Hz. Using the same formula:
Wavelength (at 20,000 Hz) = 343 m/s / 20,000 Hz
Wavelength (at 20,000 Hz) = 0.01715 meters (or 1.715 cm)
Now, moving on to the second question:
To calculate the time it takes for a dolphin to hear an echo, we need to consider the speed of sound in water and the distance traveled by the sound wave.
Given:
Speed of sound in sea water = Assume it to be 1531 m/s (at 25°C)
Distance to the bottom of the ocean = 150 m
To calculate the time, we can use the formula:
Time = Distance / Speed
Time = 150 m / (Speed of sound in sea water)
Time = 150 m / (1531 m/s)
Time ≈ 0.098 seconds
Therefore, it takes approximately 0.098 seconds for the dolphin to hear an echo after emitting a sound directed toward the bottom of the ocean.