Solving Sonar Wavelength for Bats Detecting Mosquitos

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A bat using SONAR at 50 kHz has a wavelength of approximately 6.88 mm, which is larger than the size of a 2 mm mosquito. Therefore, the bat cannot detect the mosquitoes since SONAR requires targets to be larger than one wavelength. The equation c = fλ is relevant for calculating the wavelength based on frequency. The initial equation presented, v = change in x/change in t, is not applicable in this context. The conclusion is that bats cannot detect mosquitoes due to the size limitation imposed by the wavelength.
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Homework Statement



a bat operates on SONAR system at a frequency of about 50khz. Since SONAR only responds to targets larger than one wavelength in size, can't he bat detect mosquitos that are about 2mm in size?

Homework Equations



v= change in x/change in t

The Attempt at a Solution



for 50 KHz i find the wavelength to be 6.88 mm, so the bat will not detect the small 2mm mosquitos. is this correct?
 
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looks alright to me, but I'm not sure why you posted that equation. The one you need to use and it looks like you have is c=f\lambda
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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