A. 409 Hz
The fundamental frequency of a string is given by:

where
L is the length of the wire
T is the tension in the wire
m is the mass of the wire
For the piano wire in this problem,
L = 0.400 m
T = 1070 N
m = 4.00 g = 0.004 kg
So the fundamental frequency is

B. 24
For this part, we need to analyze the different harmonics of the piano wire. The nth-harmonic of a string is given by

where
is the fundamental frequency.
Here in this case

A person is capable to hear frequencies up to

So the highest harmonics that can be heard by a human can be found as follows:

Yes, scientific method can be applied on many everyday activities to get a reasonable solution. Infact normally we are applying this method without having it in our knowledge that we are applying it.
For example: In morning we are going to office and we start the car, but it is not started.You turn the engine again and again but it simply donot works.
Observation (the state of defining a problem):
The car is not started
Hypothesis (A possible solution based on the information we already know):
The car is not started because it might be out of gas or there can be some other technical fault.
Experiment (testing of hypothesis by applying different methods of solving problem):
You get the fuel and put it inside the car but it still donot works and car didnot start. Experiment didnot get solution.
Analyze the results of data and test another hypothesis
You call a technician and he check with the car engine tries and finds out that the engine was out of order and needs repairing.
Draw conclusion:
The engine do not works when it is out of order and it is a cause of a car not being started.
<em>Now the theory and law making part can not be applied on this case but it is a part of scientific method.</em>
Hope it helps!
Answer:
Efficiency = 52%
Explanation:
Given:
First stage
heat absorbed, Q₁ at temperature T₁ = 500 K
Heat released, Q₂ at temperature T₂ = 430 K
and the work done is W₁
Second stage
Heat released, Q₂ at temperature T₂ = 430 K
Heat released, Q₃ at temperature T₃ = 240 K
and the work done is W₂
Total work done, W = W₁ + W₂
Now,
The efficiency is given as:

or
Work done = change in heat
thus,
W₁ = Q₁ - Q₂
W₂ = Q₂ - Q₃
Thus,

or

or

also,

or

thus,

thus,

or

or
Efficiency = 52%