A man is traveling on a bicycle at 14 m/s along a straight road that runs parallel to some railroad tracks. He hears the whistle of a train that is behind him. The frequency emitted by the train is 840 Hz, but the frequency the man hears is 778 Hz. Take the velocity of sound to be 340 m/s.

a) What frequency is heard by a stationary observer located between the train and the bicycle?

b) What is the speed of the train, and is the train traveling away from or towardthe bicycle?

Explanation:

b ) The problem is based on Doppler's effect of sound

f = f₀ x (V - v₀) /( )

f is apparent frequency ,f₀ is real frequency , V is velocity of sound , v₀ is velocity of observer going away  , is velocity of source going away

778  = 840 x (340 - 14)/ (340 + )

340 + = 341.18

= 1.18 m /s

it will go  away from   the observer or the cyclist.

speed of train = 1.18 m /s

a )

For a stationary observer v₀ = 0

f = f₀ x V  /( )

= 840 x 340 / (340 + 1.180)

= 837 Hz

answer: the correct answer is 1.

explanation: there are various process in which a radioactive nuclei decays:

1) alpha decay: in this process, a heavier nuclei decays into lighter nuclei by releasing alpha particle. the mass number is reduced by 4 units.

2) electron capture: in this decay process, a parent nuclei absorbs an electron and gets converted into a neutron. simply, a proton and an electron combines together to form a neutron. mass number does not change in this process.

3) gamma ray emission: it is a decay process in which an unstable nuclei gives excess energy by a spontaneous electromagnetic process. this decay releases . this process does not change the mass number.

4) positron emission: it is a type of decay process, in which a proton gets converted to neutron and an electron neutrino. this is also known as -decay. in this the mass number remains same.

from the above information, we see that only alpha-decay is producing a change in the mass number of the nucleus.

not moving. pos accel,