Given that,
Frequency emitted by the bat, f = 47.6 kHz
The speed off sound in air, v = 413 m/s
We need to find the wavelength detected by the bat. The speed of a wave is given by formula as follows :

or

So, the bat can detect small objects such as an insect whose size is approximately equal to the wavelength of the sound the bat makes i.e. 8.67 mm.
Answer:
Rate of change of magnetic flux
Explanation:
The induced current is equal to the ratio of induced emf to the resistance of the conductor.
According to the Faraday's law of electromagnetic induction, the induced emf is proportional to the rate of change of magnetic flux.
Answer:
v = 2.18m/s
Explanation:
In order to calculate the speed of Betty and her dog you take into account the law of momentum conservation. The total momentum before Betty catches her dog must be equal to the total momentum after.
Then you have:
(1)
M: mass Betty = 40kg
m: mass of the dog = 15kg
v1o: initial speed of Betty = 3.0m/s
v2o: initial speed of the dog = 0 m/s
v: speed of both Betty and her dog = ?
You solve the equation (1) for v:

The speed fo both Betty and her dog is 2.18m/s