Calculating Beat Frequencies in Identical Strings with Varying Lengths

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In summary, the two strings have a difference of 0.65 cm in length and both have a speed of 34.9 m/sec. The fundamental frequency of the shorter string is 220 Hz. To find the frequency of the beat when these strings are plucked together, the length of the longer string is calculated using the given information and then divided by the wavelength to get the new frequency. However, this method does not give the correct answer. Similarly, for a length difference of 0.8 cm, the same steps are followed but the answer is still incorrect. It is suggested to use the given equation v = fλ and find the wavelength first, then calculate the new frequency.
  • #1
wolves5
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Two strings which are fixed at both ends are identical except that one is 0.65 cm longer than the other. Waves on both of these string propagate with a speed of 34.9 m/sec and the fundamental frequency of the shorter string is 220 Hz.

a) What is frequency of the beat that would result if these two strings were plucked at the same time?

For this, I did 34.9 / 220 to get the length of the string, which was 0.158636m. Then I added 0.065m to it to get 0.2236m. Then I did, 34.9 / 0.2236 to get the new frequency which is 156.0569 Hz, but that's not right. It makes sense since the new frequency should be greater. What am I doing wrong?

c) What is the beat frequency if the length difference is now 0.8 cm?

For this one, I would pretty much follow the same steps for part a, but use 0.08m and then subtract 220 from this new frequency.
 
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  • #2
For this, I did 34.9 / 220 to get the length of the string,
This in not correct.
v = fλ.
In the fundamental mode of vibration, length of the stretched string is λ/2.
 
  • #3
So then I did 34.9 / 220 and got 0.15863 for the wavelength. Then I divided that by 2 and got 0.0793. After that, do I follow the same steps as I desctibed in the problem?
 
  • #4
Ok, so I used this new answer and followed the same steps as I described earlier and its still not the right answer. My answer was 241.927. Its greater than the original frequency, but still not the right answer.
 
  • #5
0.65 cm = 0.0065 m.
 
  • #6
Ok, so I added 0.0065 to 0.079318m and got 0.085818m. Then I did 34.9/ 0.085818 and got 406.6737 Hz, but that's not right either.
 
  • #7
Length of the wire is 0.085818 = λ/2.
Find λ and then frequency.
 

FAQ: Calculating Beat Frequencies in Identical Strings with Varying Lengths

What is "Beats from Different Strings"?

"Beats from Different Strings" is a phenomenon that occurs when two strings of slightly different frequencies are played simultaneously. This results in a pulsing sound, or "beats", as the waves of the two strings interfere with each other.

What causes "Beats from Different Strings"?

The phenomenon of "Beats from Different Strings" is caused by the interference of sound waves. When two strings of slightly different frequencies are played at the same time, the waves they produce will occasionally align and reinforce each other, resulting in a louder sound, and other times they will cancel each other out, resulting in a softer sound. This creates the pulsing effect known as "beats".

How are "Beats from Different Strings" used in music?

Musicians can use "Beats from Different Strings" intentionally to create a unique sound in their music. By playing two strings of different frequencies, the beats produced can add texture and depth to a piece of music. This technique is often used in classical and experimental music.

Can "Beats from Different Strings" be heard with any type of instrument?

Yes, "Beats from Different Strings" can occur with any type of instrument, as long as it produces sound waves. This includes string instruments, such as guitars and violins, as well as wind instruments, such as flutes and clarinets.

How can "Beats from Different Strings" be calculated or measured?

The frequency of beats produced by two strings can be calculated by subtracting the frequencies of the two strings. For example, if one string has a frequency of 200 Hz and another has a frequency of 205 Hz, the resulting beats will have a frequency of 5 Hz. This can also be measured using a tuning fork or electronic tuner.

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