Learning object 7: Beats Questions on the concepts behind beats, and guide through the setting up of the equation for the resulting wave of two separate waves.

1. You are teaching a band class of high school students.
1. You ask two out of tune trumpet players to play the same note. When instruments are out of
tune, it means that the frequency of the instruments are different. What do you hear?
2. If one student’s instrument has a frequency of 125 Hz, and the other with a frequency of 116
Hz, what is the beat frequency?
3. What is the mean angular frequency of the two instruments, knowing their frequencies from
question 2?
4. What is the angular frequency difference of the two instruments?
5. Using the values calculated in questions 3 and 4, find the equation for the resulting wave if sm
= 2 and x0 = 0.
6. How does beat frequency relate to the frequency you hear in question 2?
7. The two students tune their instruments so that they are very close in frequency. You then ask
them to play together again. What do you hear now?

2. Answers:
1.You ask two out of tune trumpet players to play the same note. When instruments are out of
tune, it means that the frequency of the instruments are different. What do you hear?
You hear the modulated “beating” sound, due to the alternating constructive and destructive
interference. It sounds as an alternating soft-loud sound.
2. If one student’s instrument has a frequency of 125 Hz, and the other with a frequency of 116
Hz, what is the beat frequency?
The beat frequency is the absolute value of the difference between the two frequencies. So:
fbeat = | f1 - f2 | = | 125 Hz - 116 Hz | = 9 Hz
The beat frequency is 9 Hz.
3. What is the mean angular frequency of the two instruments, knowing their frequencies from
question 2?
Mean angular frequency can be determined using the formula
and inputting the given values.
Therefore, the mean angular frequency is 120.5 Hz
4. What is the angular frequency difference of the two instruments?
The angular frequency difference can be evaluated using the formula
and inputting the given values
Therefore, the angular frequency difference is 4.5 Hz.
5. Using the values calculated in questions 3 and 4, find the equation for the resulting wave if
s_m = 2 and x0 = 0.
The equation for the resulting wave where x0 = 0 is given by
Inserting the values from questions 3 and 4:
6. How does beat frequency relate to the frequency you hear in question 2?
What you hear in question 2 is the average frequency of the two instruments, which results from
them being very close in frequency. The sum of the two played notes is the average frequency.
This is much larger than the beat frequency. So, average frequency >> beat frequency.
7.The two students tune their instruments so that they are very close in frequency. You then ask
them to play together again. What do you hear now?
You hear one note: the average frequency.