**Explanation:**

When a transformer is operated at a frequency other than its rated frequency, the humming noise produced by the transformer changes.

**1. Magnetic Flux:**

The magnetic flux in a transformer is directly proportional to the voltage and inversely proportional to the frequency. So, when the frequency is decreased from the rated frequency, the magnetic flux in the transformer increases.

**2. Core Losses:**

The core losses in a transformer are made up of hysteresis losses and eddy current losses. Hysteresis losses occur due to the reversal of magnetization in the core material, and eddy current losses occur due to circulating currents induced in the core.

Both hysteresis losses and eddy current losses are directly proportional to the frequency. So, when the frequency is reduced, the core losses decrease.

**3. Electrical Losses:**

The electrical losses in a transformer are made up of copper losses and stray losses. Copper losses occur due to the resistance of the transformer windings, and stray losses occur due to leakage flux and other factors.

Copper losses are directly proportional to the square of the current and frequency, while stray losses are directly proportional to the square of the voltage and frequency. So, when the frequency is reduced, both the copper losses and stray losses decrease.

**4. Mechanical Vibrations:**

The mechanical vibrations or humming noise produced by a transformer are caused by the magnetostriction effect, which is the expansion and contraction of the transformer core due to the alternating magnetic field.

The magnetostriction effect is directly proportional to the square of the magnetic flux density and the frequency. So, when the frequency is reduced, the magnetostriction effect decreases, and consequently, the humming noise produced by the transformer decreases.

Therefore, when a 400 V, 10 KVA transformer is operated at a frequency of 40 Hz instead of the rated frequency of 50 Hz, the humming noise produced by the transformer decreases.