Frequency of the tuning fork:
The frequency of the tuning fork is given as 400 Hz. This means that the tuning fork completes 400 vibrations or cycles in one second.

Speed of sound in air:
The speed of sound in air is given as 350 m/s. This means that sound waves travel at a speed of 350 meters per second in air.

Finding the distance traveled by sound:
To find the distance traveled by sound while the tuning fork makes 15 vibrations, we need to calculate the time taken for 15 vibrations and then multiply it by the speed of sound.

Calculating the time taken for 15 vibrations:
The time taken for one vibration is the inverse of the frequency. So, the time taken for 15 vibrations can be calculated by multiplying the time taken for one vibration by 15.

Time taken for one vibration = 1 / Frequency = 1 / 400 Hz = 0.0025 seconds

Time taken for 15 vibrations = 0.0025 seconds * 15 = 0.0375 seconds

Calculating the distance traveled by sound:
Now that we have the time taken for 15 vibrations, we can calculate the distance traveled by sound by multiplying it by the speed of sound.

Distance traveled by sound = Speed of sound * Time taken = 350 m/s * 0.0375 seconds = 13.125 meters

Therefore, the sound travels a distance of 13.125 meters while the tuning fork makes 15 vibrations.

Summary:
- The frequency of the tuning fork is given as 400 Hz.
- The speed of sound in air is given as 350 m/s.
- To find the distance traveled by sound while the tuning fork makes 15 vibrations, we calculated the time taken for 15 vibrations and multiplied it by the speed of sound.
- The time taken for 15 vibrations is calculated by multiplying the time taken for one vibration (inverse of the frequency) by 15.
- The distance traveled by sound is calculated by multiplying the speed of sound by the time taken for 15 vibrations.
- Therefore, the sound travels a distance of 13.125 meters while the tuning fork makes 15 vibrations.