To solve this problem we apply the thermodynamic equations of linear expansion in bodies.
Mathematically the change in the length of a body is subject to the mathematical expression

Where,
Initial Length
Thermal expansion coefficient
Change in temperature
Since we have values in different units we proceed to transform the temperature to degrees Celsius so


The coefficient of thermal expansion given is

The initial length would be,

Replacing we have to,




This means that the building will be 35.5cm taller
Answer:
(i) The wavelength is 0.985 m
(ii) The frequency of the wave is 36.84 Hz
Explanation:
Given;
mass of the string, m = 0.0133 kg
tensional force on the string, T = 8.89 N
length of the string, L = 1.97 m
Velocity of the wave is:

(i) The wavelength:
Fourth harmonic of a string with two nodes, the wavelength is given as,
L = 2λ
λ = L/2
λ = 1.97 / 2
λ = 0.985 m
(ii) Frequency of the wave is:
v = fλ
f = v / λ
f = 36.29 / 0.985
f = 36.84 Hz
Answer:
4°C
Explanation:
Water is densest at 4°C. Since dense water sinks, the bottom of the lake will be 4°C.