Will humans be able to hear a sound that has a wavelenth of 26.314 m (57 Hz, 1500 m/s)? Explain?
If a dolphin sends out an ultrasound underwater toward a boat and the sound returns in 1 second, how far away is the boat?
The human ear USUALLY is listed as hearing 20 Hz to 20,000 Hz but those numbers vary with individuals. As we age the high frequency hearing falls off dramatically. When I was younger, I could hear 19,000 Hz but not that high now. Most people can hear 60 Hz easily.
They would if 1500 m/s were the speed of sound, which is what you stated. The actual speed of sound is much less than that, so that wavelength would NOT be heard.
If 26 m were the true wavelength and you used the correct speed of sound of in air about 300 m/s, the frequency would be 300/26 = 11 Hz, which cannot be heard. However, if the sound is being transmitted under water, the sound speed is about right and it is the frequency that determines if it can be heard.
If 57 Hz is the true frequency, that can be heard by most people.
For the second part of your question, 0.5 seconds is the one-way sound travel time from dolphin to boat, so the distance is 0.5 s* 1500 m/s = 750 m
To determine whether humans can hear a sound with a specific wavelength, we need to consider the range of audible frequencies for humans.
The audible frequency range for humans is generally considered to be between 20 Hz and 20,000 Hz (or 20 kHz). The sound you mentioned has a frequency of 57 Hz, which falls within the audible range for humans. Therefore, humans can potentially hear a sound with this frequency.
However, it's important to note that the wavelength (26.314 m) is quite long for an audible sound. In normal conditions, sound waves with such long wavelengths may not efficiently propagate through air, causing the sound to be weak and difficult to hear.
Regarding the second question about the distance between a dolphin and a boat, we can use the speed of sound in water to calculate the distance.
The speed of sound in water is approximately 1500 m/s. Given that the sound sent by the dolphin returns in 1 second, we can conclude that the sound traveled a total distance of 1500 meters (since speed = distance/time).
Therefore, the boat is located approximately 1500 meters away from the dolphin.