Why are low beats more audible than high beats

  • Thread starter brandy
  • Start date
In summary, the difference in frequencies between two consecutive low notes is smaller than the difference in frequencies between two consecutive high notes, which makes the beats more audible. This is due to the factor of 2^(1/12) increase in frequency for each step in a sequence of notes.
  • #1
brandy
161
0
question: "why are beats more audilbe between two consecutive low notes than two consecutive high notes? support your answer with relevant calculations and explanation?"
we were given some rules first:
theres
sin(2pi*h)t
(the formula for a sound wave, h=hz and t=the x value when graphing)

(2 sin*((2pi*hi )t+(2pi*hii )t)/2)×cos*((2pi*hi )t-(2pi*hii )t)/2)
where hi is the frequency of one tone and hii is the frequency of the sequential tone.

i remembered that 2^(1/12) would be the difference between them and i still need help explaining why

any help is muchly appreciated
 
Physics news on Phys.org
  • #2
Hi brandy,

The difference is 2^(1/12) because they say consecutive notes; for example, think of consecutive keys on a piano. When you go from one C note to the next higher C, you have to cover 12 keys. And when you go from one C to the next C, the frequency doubles. So the frequency at each steps goes up by a factor of 2^(1/12).

To answer your question, you might think about what is the difference in frequencies between two consecutive low notes, and between two consecutive high notes, since it is the small difference in frequencies that give rise to (regular) beats.
 
  • #3


The reason why low beats are more audible than high beats can be explained through the concept of beat frequency. Beat frequency refers to the difference in frequency between two consecutive notes that are played together. It is calculated by subtracting the frequency of the lower note from the frequency of the higher note.

In the given formula, we can see that the amplitude of the sound wave is multiplied by the cosine of the difference in frequency between the two notes. This means that the amplitude of the sound wave will be affected by the difference in frequency between the two notes.

Now, let's consider two consecutive low notes with frequencies hi and hii, where hii is slightly higher than hi. The beat frequency in this case would be hii-hi, which would result in a small difference in frequency. As a result, the cosine term in the formula would be close to 1, which means that the amplitude of the sound wave would not be affected much. This results in a clear and audible beat between the two notes.

On the other hand, if we consider two consecutive high notes with frequencies hi and hii, where hii is significantly higher than hi, the beat frequency would be hii-hi, which would result in a larger difference in frequency compared to the previous case. This would result in a smaller value for the cosine term, which means that the amplitude of the sound wave would be affected more. As a result, the beat between the two notes would be less audible.

Furthermore, the difference in frequency between two consecutive low notes is smaller compared to the difference between two consecutive high notes. This is because the frequency of a sound wave increases exponentially with an increase in pitch. For example, the frequency of a note one octave above a low note would be double the frequency of the low note. This means that the difference in frequency between two consecutive low notes would be smaller compared to the difference between two consecutive high notes.

In conclusion, the reason why low beats are more audible than high beats is because of the smaller difference in frequency between two consecutive low notes, resulting in a larger value for the cosine term in the formula and a more audible beat.
 

1. Why do low beats sound louder than high beats?

Low beats have a longer wavelength, which means they carry more energy and travel further. This makes them easier to detect and hear compared to high beats with shorter wavelengths and less energy.

2. How does the human ear perceive low beats differently from high beats?

The human ear has specialized hair cells that vibrate in response to sound waves. These cells are more sensitive to low frequencies, making them easier to detect and interpret compared to high frequencies.

3. Why do low beats carry more energy than high beats?

The amount of energy carried by a sound wave is determined by its amplitude, or height. Low beats have a larger amplitude compared to high beats, which means they carry more energy and can be perceived as louder.

4. Are low beats always more audible than high beats?

In general, yes, low beats are more audible than high beats. However, this can vary depending on other factors such as the environment and individual hearing abilities. In some cases, high beats may be more audible due to their sharp and distinct sound.

5. Can high beats be made more audible than low beats?

Yes, high beats can be made more audible through amplification or by increasing their amplitude. However, this may also result in distortion and discomfort for the listener. It is generally recommended to maintain a balanced mix of low and high frequencies for optimal sound perception.

Similar threads

  • Introductory Physics Homework Help
Replies
3
Views
161
Replies
3
Views
451
  • Introductory Physics Homework Help
2
Replies
43
Views
5K
Replies
23
Views
6K
  • Introductory Physics Homework Help
Replies
3
Views
768
  • Introductory Physics Homework Help
Replies
3
Views
699
  • Introductory Physics Homework Help
Replies
7
Views
2K
  • Introductory Physics Homework Help
Replies
1
Views
1K
Replies
9
Views
1K
  • Introductory Physics Homework Help
Replies
6
Views
1K
Back
Top