The response is 176 minutes. The translation of 456 g equals 0.456 kg. The specific heat of ice is 2093 J kg⁻¹, used to calculate heat required for a 25-degree rise, determined by mass multiplied by specific heat and temperature increase. The necessary calculations yield a total heat load of 176164 J. Finally, by dividing heat required by heat supply rate, we ascertain that it will take approximately 176.16 minutes.
The question pertains to the change in frequency of a wave noted by an observer moving in relation to the source, indicating that the concept to invoke is "
Doppler's effect."
The standard formula for the Doppler effect is:

-- (A)
Note that we don’t need to be concerned with the signs here, as all entities are moving toward each other. If something was moving away, a negative sign would apply, but that is not relevant to this scenario.
Where,
g = Speed of sound = 340m/s.

= Velocity of the observer relative to the medium =?.

= Velocity of the source in relation to the medium = 0 m/s.

= Frequency emitted from the source = 400 Hz.

= Frequency recognized by the observer = 408 Hz.
Substituting the given values into equation (A) will yield:


Solving the above will result in,

= 6.8 m/s
The correct result = 6.8m/s
The sheet's thickness is calculated to be t= 0.0003 mm.
The mass provided is m = 230 mg, equivalent to 0.23 g. The area of the sheet is A= 23 x 17 cm², totaling A= 391 cm². Given the density of gold is ρ = 19.32 g/cm³, we assume the sheet's thickness is t cm. From the equation Mass = Density x Volume, we know m = ρ A t. Substituting the values results in:
0.23 = 19.32 × 391 × t, leading to t = 0.000030 cm, or equivalently, 0.0003 mm as the final thickness.