Answer:
1.21m
Explanation:
If two speakers are generating a frequency of 280Hz, the smallest separation distance between the speakers that will produce destructive interference at a listener standing in front of them is also known as the wavelength of the sound wave generated.
Using the expression;
Velocity v = frequency f × wavelength ¶
Given frequency = 280Hz, speed of sound v = 338m/s
Substituting this data's in the expression given to get the wavelength will give;
¶ = v/f
¶ = 338/280
¶ = 1.21m
The smallest separation between the speakers that will produce the interference is 1.21m
A) 4.7 cm
The formula for the angular spread of the nth-maximum from the central bright fringe for a diffraction from two slits is

where
n is the order of the maximum
is the wavelength
is the distance between the slits
In this problem,
n = 5


So we find

And given the distance of the screen from the slits,

The distance of the 5th bright fringe from the central bright fringe will be given by

B) 8.1 cm
The formula to find the nth-minimum (dark fringe) in a diffraction pattern from double slit is a bit differente from the previous one:

To find the angle corresponding to the 8th dark fringe, we substitute n=8:

And the distance of the 8th dark fringe from the central bright fringe will be given by

Kinetic energy lost in collision is 10 J.
<u>Explanation:</u>
Given,
Mass,
= 4 kg
Speed,
= 5 m/s
= 1 kg
= 0
Speed after collision = 4 m/s
Kinetic energy lost, K×E = ?
During collision, momentum is conserved.
Before collision, the kinetic energy is

By plugging in the values we get,

K×E = 50 J
Therefore, kinetic energy before collision is 50 J
Kinetic energy after collision:


Since,
Initial Kinetic energy = Final kinetic energy
50 J = 40 J + K×E(lost)
K×E(lost) = 50 J - 40 J
K×E(lost) = 10 J
Therefore, kinetic energy lost in collision is 10 J.