Question

A dolphin is able to tell in the dark that the ultrasound echoes received from two sharks come from two different objects only if the sharks are separated by 3.50 m. (a) If the ultrasound has a frequency of 100 kHz, show this ability is not limited by its wavelength.

a) The wavelength is negligible compared to the separation.
b) The wavelength is significant but not limiting.
c) The wavelength is the limiting factor.
d) The ability is not influenced by wavelength.

Answer 1

The dolphin's ability to differentiate between two sharks is given by a wavelength that is negligible compared to the separation distance, which is further supported by the minimum time difference the dolphin can perceive when echoes reflect from the sharks.

Step-by-step explanation:

To determine if the dolphin's ability to differentiate between the two sharks is not limited by wavelength, we need to calculate the wavelength of the ultrasound and compare it to the separation distance.

Calculating the Wavelength

The speed of sound in seawater is approximately 1500 m/s. The wavelength (λ) can be found using the relationship λ = v/f, where v is the speed of sound and f is the frequency.

λ = 1500 m/s / 100000 Hz = 0.015 m

Since the wavelength (0.015 m) is much smaller than the separation distance (3.50 m), we can conclude that the dolphin's ability is not limited by the wavelength. This is option (a): The wavelength is negligible compared to the separation.

Minimum Time Difference Perception

For part (b), the minimum time difference the dolphin can perceive is based on the distance the sound travels in water. The distance d = v ⋅ t, so to detect a 3.50 m difference, the minimum time is:

t = d/v = 3.50 m / 1500 m/s = 0.00233 s or 2.33 ms

Therefore, the minimum time difference the dolphin can perceive would be 2.33 milliseconds.