Answer:
Part 1:
Option B is correct (It will remain unchanged).
Part 2:
Option C is correct (It will increase by a factor of √ 2)
Part 3:
Option E is correct (It will be half as fast/long.)
Part 4:
Option C is correct (It will increase by a factor of √ 2.)
Explanation:
Formula we are going to use:
V=f*λ
Where:
V is the speed of Sound
f is the frequency of wave
λ is the wavelength.
The speed of wave , tension and linear density have following relation:
Where:
V is the speed of Sound (Initial)
F is the tension in string (Initial)
is the linear density of string (Constant)
Terms:
V' is the new speed
f' is the new frequency
λ' is the wavelength
Solution:
Part 1:
From :
Speed of Sound is independent of the frequency of shaking so speed well remain unchanged.
Option B is correct (It will remain unchanged)
Part 2:
If F'=2F then
Option C is correct (It will increase by a factor of √ 2)
Part 3:
Formula we are going to use:
V=f*λ
Given f'=2f,
Even though frequency is doubled we will keep velocities same. V=V' in order to find the changing wavelength.
V'=f'*λ'
f*λ=f'*λ'
f*λ=2f*λ'
Solving above Equation:
λ'=λ/2
Option E is correct (It will be half as fast/long.)
Part 4:
T'=2T means 
(From Part 1)
f'=f
Now:
V'=f'*λ'
Option C is correct (It will increase by a factor of √ 2.)
