Which one of the following frequency can set the string into resonant vibration?

If a guitar string has a fundamental frequency of 500Hz

a)250Hz
b)750Hz
c)1500Hz
d)1750Hz

It has to be an integral multiple of 500 Hz. Only one of those frequencies meets that requirement.

what does that mean?

The ratio of a resonant frequency to 500 Hz (the fundamental) must be an integer. That is only true for one of the four choices.

That is what it means.

ITS C

To determine which of the given frequencies can set the string into resonant vibration, we need to understand the concept of resonance. Resonance occurs when an object vibrates at its natural frequency or a harmonic of its natural frequency.

The fundamental frequency of the guitar string is 500Hz. This means that when it vibrates freely, it produces a sound wave with a frequency of 500Hz.

Now, let's analyze each of the given frequencies:

a) 250Hz: This frequency is exactly half the fundamental frequency. It is known as the first harmonic or the second overtone. It can set the string into resonant vibration because it is a harmonic of the fundamental frequency.

b) 750Hz: This frequency is one and a half times the fundamental frequency. It is known as the third harmonic or the fourth overtone. It can also set the string into resonant vibration because it is a harmonic of the fundamental frequency.

c) 1500Hz: This frequency is three times the fundamental frequency. It is known as the sixth harmonic or the seventh overtone. It can set the string into resonant vibration because it is a harmonic of the fundamental frequency.

d) 1750Hz: This frequency is 3.5 times the fundamental frequency. It is not a harmonic of the fundamental frequency, so it cannot set the string into resonant vibration.

Therefore, the correct answer is a) 250Hz, b) 750Hz, and c) 1500Hz. These frequencies can all set the guitar string into resonant vibration.