Two strings are vibrating at the same frequency of 113 Hz. After the tension in one of the strings is decreased, an observer hears two beats each second when the strings vibrate together. Find the new frequency in the adjusted string.
236
To find the new frequency in the adjusted string, we need to understand the concept of beats.
Beats occur when two sound waves of slightly different frequencies interfere with each other. This interference creates a periodic increase and decrease in the overall amplitude of the sound. The number of beats heard per second is equal to the difference in frequencies between the two sound waves.
In this scenario, initially, the two strings were vibrating at the same frequency of 113 Hz. However, after decreasing the tension in one of the strings, we start hearing two beats each second when the strings vibrate together.
Now, we can use this information to determine the new frequency in the adjusted string as follows:
1. Let's assume the original frequency of the adjusted string is "f" Hz.
2. The other string's frequency remains the same at 113 Hz.
3. Since we hear two beats per second, the difference in frequencies between the two strings will be 2 Hz (two beats).
4. Therefore, the equation becomes: f - 113 Hz = 2 Hz.
Solving the equation for "f", we have:
f = 113 Hz + 2 Hz
f = 115 Hz
So, the new frequency in the adjusted string is 115 Hz.