Bats chirp at high frequencies that humans cannot hear. They use the echoes to detect small objects, such as insects, as small as one wavelength. If a bat emits a chirp at a frequency of 60.0 kHz and the speed of sound waves in air is 340 m/s, whar is the size in millimeters of the smallest insect that the bat can detect?
I know the answer is 5.7mm but not sure how to get to it someone help pls.
period = 1/f = 1/60,000
= 1.67*10^-5 second
goes one wavelength in one period
distance = speed * time
so
wavelength = 340*1.67*10^-5
= .00566 meters
= 5.67 millimeters
To calculate the size of the smallest insect that a bat can detect, we need to determine the wavelength of the sound wave emitted by the bat.
First, we can use the formula for wave speed:
v = λ * f
Where:
v = speed of sound wave in air = 340 m/s
λ = wavelength of the sound wave
f = frequency of the sound wave emitted by the bat = 60.0 kHz = 60,000 Hz
Rearranging the equation, we can solve for the wavelength:
λ = v / f
Now we can plug in the values:
λ = 340 m/s / 60,000 Hz
To convert the wavelength to millimeters, we need to multiply it by 1,000:
λ = (340 m/s / 60,000 Hz) * 1,000 = 5.7 mm
Therefore, the size in millimeters of the smallest insect that the bat can detect is approximately 5.7 mm.
To find the size of the smallest insect that the bat can detect, we need to determine the wavelength of the sound waves emitted by the bat. We can use the formula:
Wavelength = Speed of sound / Frequency
Substituting the given values:
Wavelength = 340 m/s / 60,000 Hz
Now, we need to convert the wavelength to millimeters. Since there are 1000 millimeters in a meter, we can multiply the value by 1000:
Wavelength = (340 m/s / 60,000 Hz) * 1000 = 5.67 mm
Therefore, the size of the smallest insect the bat can detect is approximately 5.7 mm.