A string has a length of 2.50 m and is fixed at the ends. At a frequency of 85.0 Hz, a standing wave with 5 loops is formed.
I got a, b and d. I need help with c and e thank you
a. What is the wavelength of the waves that travel on the string? (i did this already)
b. What is the speed of the waves? (i did this already)
c. What is the wavelength of the wave when it is vibrating at the fundamental frequency of the wave? (i need to know this)
d. What is the fundamental frequency of the wave? (i did this already)
e. At what frequency would the third overtone occur? (i need to know this)
c. I dont know what you mean by 5 loops, but if you mean a wavelength, then divide 2.50m by 5
e. multipy d by 3.
An example of harmonic overtones: (absolute harmony) and various names given to them.
Frequency Order Name 1 Name 2 Name 3
1 · f = 440 Hz n = 1 fundamental tone 1st harmonic 1st partial
2 · f = 880 Hz n = 2 2nd overtone[4] 2nd harmonic 2nd partial
3 · f = 1320 Hz n = 3 3rd overtone 3rd harmonic 3rd partial
4 · f = 1760 Hz n = 4 4th overtone 4th harmonic 4th partial
c. What is the wavelength of the wave when it is vibrating at the fundamental frequency of the wave?
Hmm, let me think about this... So, we know that the frequency of the wave is 85.0 Hz. Since we already calculated the speed of the waves in part b, we can use the formula v = f * λ (where v is the speed, f is the frequency, and λ is the wavelength) to find the wavelength when vibrating at the fundamental frequency.
Since we have the speed and the frequency, we can rearrange the formula to solve for λ. Trust me, rearranging formulas can be quite fun, just like rearranging the furniture in your living room!
Anyway, let's plug in the values. We have v = speed of the wave (which you calculated already) and f = 85.0 Hz (the fundamental frequency). Solving for λ, we get:
λ = v / f
Just substitute the values and calculate the wavelength, and you'll have your answer for part c! Remember, math is like a clown juggling different numbers, but with the right steps, it can be a hilarious show!
e. At what frequency would the third overtone occur?
Ah, the third overtone! I guess it's like the third clown at a circus, always bringing some extra fun to the party!
To find the frequency of the third overtone, we need to know the fundamental frequency and then apply a simple multiplication. The third overtone frequency is three times the fundamental frequency. So, take the fundamental frequency (which you already calculated) and multiply it by three! Ta-da! That gives you the frequency of the third overtone.
Just remember, in the world of physics and clowning around, third times the charm!
c. To find the wavelength of the wave when it is vibrating at the fundamental frequency of the wave, you can divide the length of the string by the number of loops.
Given:
Length of string (L) = 2.50 m
Number of loops (n) = 5
Wavelength of the wave at the fundamental frequency (λ1) = L / n
Substituting the values:
λ1 = 2.50 m / 5
Simplifying the expression:
λ1 = 0.50 m
So, the wavelength of the wave when it is vibrating at the fundamental frequency of the wave is 0.50 m.
e. To find the frequency at which the third overtone occurs, you can use the formula:
Frequency of the nth overtone (fn) = (2n - 1) * Fundamental frequency
Given:
Fundamental frequency of the wave (f1) = 85.0 Hz
Number of the overtone (n) = 3
Frequency of the third overtone (f3) = (2 * 3 - 1) * 85.0 Hz
Simplifying the expression:
f3 = 5 * 85.0 Hz
f3 = 425 Hz
So, the frequency at which the third overtone occurs is 425 Hz.
c. To find the wavelength of the wave when it is vibrating at the fundamental frequency, you can use the formula: wavelength = 2 * length / number of loops.
In this case, the length of the string is given as 2.50 m, and the number of loops is 5 (since it is vibrating at the fundamental frequency).
So, the wavelength would be: wavelength = 2 * 2.50 m / 5 = 1.00 m.
Therefore, the wavelength of the wave when it is vibrating at the fundamental frequency is 1.00 m.
e. To find the frequency of the third overtone, you need to understand that the overtone frequencies form a harmonic series. In a harmonic series, each successive overtone has a frequency that is a multiple of the fundamental frequency.
The fundamental frequency is given as 85.0 Hz. To find the frequency of the third overtone, you can use the formula: frequency of the nth overtone = n * fundamental frequency.
In this case, n = 3 (for the third overtone).
So, the frequency of the third overtone would be: frequency of the third overtone = 3 * 85.0 Hz = 255.0 Hz.
Therefore, the frequency of the third overtone is 255.0 Hz.