Explanation:

To determine the number of pulses per half cycle of the output signal in sinusoidal pulse width modulation (SPWM), we need to understand the relationship between the harmonics and the number of pulses.

Harmonics in SPWM:
In SPWM, the modulated signal is a combination of multiple harmonics. The lowest-order harmonic in the modulated signal determines the number of pulses per half cycle. Let's assume the lowest-order harmonic is the nth harmonic.

Relationship between Harmonics and Number of Pulses:
In SPWM, the modulated signal is created by comparing the amplitude of a carrier signal with the amplitude of a reference sinusoidal signal. The duty cycle of each pulse in the modulated signal corresponds to the instantaneous value of the reference signal.

The number of pulses per half cycle of the output signal is equal to the number of times the reference signal crosses the carrier signal during one half cycle. This is because each crossing of the reference signal corresponds to a pulse in the modulated signal.

If the lowest-order harmonic in the modulated signal is the nth harmonic, it means that the reference signal crosses the carrier signal n times during one half cycle.

Determining the Number of Pulses:
In the given question, it is mentioned that the lowest-order harmonic in the modulated signal is the 15th harmonic. This means that the reference signal crosses the carrier signal 15 times during one half cycle.

To determine the number of pulses, we need to find the number of times the reference signal crosses the carrier signal above and below the zero reference line.

Since each crossing corresponds to a pulse, we count the number of crossings from the zero reference line up to the highest point, and then count the number of crossings from the highest point back to the zero reference line.

In this case, the reference signal crosses the carrier signal 7 times above the zero reference line and 7 times below the zero reference line, resulting in a total of 14 crossings.

Therefore, the number of pulses per half cycle of the output signal is 14, which is equal to 7 pulses per half cycle.

Conclusion:
The correct answer is '7' pulses per half cycle of the output signal. This is determined by the number of times the reference signal crosses the carrier signal, which is given by the lowest-order harmonic in the modulated signal.