Beat Frequency of xylophone

[BuBbLeS01]

Homework Statement

A xylophone has a set of vibrating bars. A bar with a frequency of 343 Hz is struck. A very short time later, a second bar is also sounded, and one hears the volume of the xylophone increase and decrease 5 times each second (called beats). What are the possible frequencies of the second bar (in Hz)? Determine if the following frequencies is correct or incorrect.
A. 353
B. 338
C. 333
D. 348
E. 349

Homework Equations

The Attempt at a Solution

How do I figure this out?
A.
B.
C.
D.
E.

 

[BuBbLeS01]

Nevermind I got it..a lot easier then I was making it hehe.

 

[ogb p]

I would approach this problem by first understanding the concept of beat frequency. Beat frequency is the difference between the frequencies of two sound waves that are played simultaneously. In this case, the first bar has a frequency of 343 Hz, and we are looking for the frequency of the second bar that will create a beat frequency of 5 Hz (5 beats per second).

To determine the possible frequencies of the second bar, we can use the formula for beat frequency: f_beat = |f1 - f2|. Since we know f1 = 343 Hz and f_beat = 5 Hz, we can rearrange the formula to solve for f2: f2 = f1 - f_beat.

Substituting in the values, we get f2 = 343 Hz - 5 Hz = 338 Hz. This means that the frequency of the second bar can be either 338 Hz or any other frequency that is 5 Hz lower or higher than 338 Hz.

Now, let's check the given frequencies and see which one is correct:
A. 353 Hz: This frequency is 10 Hz higher than the calculated value of 338 Hz, which would result in a beat frequency of 15 Hz, not 5 Hz. Therefore, it is incorrect.
B. 338 Hz: This frequency matches the calculated value and would result in a beat frequency of 0 Hz (no beats), which is not what we are looking for. Therefore, it is also incorrect.
C. 333 Hz: This frequency is 5 Hz lower than the calculated value of 338 Hz, which would result in a beat frequency of 5 Hz, matching our desired result. Therefore, it is correct.
D. 348 Hz: This frequency is 10 Hz higher than the calculated value of 338 Hz, which would result in a beat frequency of 15 Hz, not 5 Hz. Therefore, it is incorrect.
E. 349 Hz: This frequency is 11 Hz higher than the calculated value of 338 Hz, which would result in a beat frequency of 16 Hz, not 5 Hz. Therefore, it is also incorrect.

In conclusion, the possible frequency of the second bar is 333 Hz to create 5 beats per second with the first bar with a frequency of 343 Hz.