A wire is stretched between two posts. Another wire is stretched between two posts that are four times as far apart. The tension in the wires is the same, and they have the same mass. A transverse wave travels on the shorter wire with a speed of 290 m/s. What would be the speed of the wave on the longer wire?

The speed of the wave on the longer wire is 580m/s

Explanation:

The velocity possessed by a stretched string is directly proportional to the tension in the string and inversely proportional to the mass per unit length of the string. Mathematically,

V = √T/m

Where V is the velocity of wave in the wire

T is the tension in the wire

M is the mass per unit length of the wire

Let m1 and m2 be the mass per unit length of the wires

Let T1 and T2 be their respective tensions

Since the tension and mass of the wire is the same

m1= m2= m.

T1=T2=T

Let m1 =M/l

m2 =M/4l( since the second is tour times as far apart)

V1 = 290m/s(velocity in shorter wire)

V2 is the velocity of the longer wire.

V1 = √T/(m/l)

290 = √Tl/m

290² = Tl/m... 1

V2 = √4Tl/m

V2²= 4Tl/m... 2

Dividing equation 1 by 2 we have;

290²/V2² = {Tl/m}/{4Tl/m}

290²/V2² = Tl/m × m/4Tl

290²/V2² = 1/4

Cross multiplying we have;

V2² = 290²×4

V2 = √290²×4

V2 = 290×2

V2 = 580m/s

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.

prolly a beacuse the momentuem the car has increases while going down hill