Dolphins ca detect small fish whose size is about equal to the wavelength of the sound the dolphin makes with its echo-location system. A dolphin emits a chirp at a frequency of 220 kHz. Using the speed of water as 1530 m/s, what is the smallest fish this dolphin can detect.
speed of sound = frequency x wavelength.
Substitute 220,000 for frequency. Plug in speed of sound and calculate wavelength.
To determine the smallest fish that a dolphin can detect using its echolocation system, we need to calculate the wavelength of the sound produced by the dolphin.
The formula to calculate the wavelength (λ) is:
λ = v/f
Where:
λ = wavelength of the sound
v = speed of sound in water
f = frequency of the sound
In this case, the speed of sound in water is given as 1530 m/s and the frequency of the dolphin's chirp is 220 kHz, which we'll need to convert to Hz.
1 kHz = 1000 Hz
So the frequency in Hz will be:
220 kHz * 1000 = 220,000 Hz
Now we can calculate the wavelength using the formula:
λ = 1530 m/s / 220,000 Hz
λ = 0.006955 meters or 6.955 mm
Therefore, the smallest fish that this dolphin can detect using its echolocation system is approximately 6.955 mm in size.