If the string on a violin is 25.4cm long and produces a fundamental tone of frequency of 440Hz, by how much must it be shortened to produce a fundamental tone of frequency of 523.3Hz.
is there a specific formula to follow? like, how do you know what to do?
fundamental length is 1/2 wavelength long.
so if the freq changes by 523.3/440, then lambda changes by the inverse factor, so new length is
1/2 *origlamnda*440/523.3
where orig lambda is 2*25.4cm
i don't think 47% is correct number, eslpeiacly when we paid attention to massive vote fraud with huge numbers like 141% in Florida (along with other key states. if not fraud (if it's really massive) Romney should win that election
To determine the amount by which the string should be shortened to produce a specific frequency, we can use the formula for the frequency of a vibrating string:
f = (1/2L) * sqrt(T/μ)
Where:
- f is the fundamental frequency (Hz)
- L is the length of the string (m)
- T is the tension in the string (N)
- μ is the linear mass density of the string (kg/m)
In this case, we have the initial frequency (440Hz) and the initial length (25.4cm = 0.254m). We want to find the new length and the new frequency (523.3Hz). We can assume that the tension and linear mass density remain constant.
First, we can rearrange the formula to solve for the length:
L = (1/2f) * sqrt(T/μ)
Let's substitute the initial frequency and length values into the formula to find the initial length:
L_initial = (1/2 * 440Hz) * sqrt(T/μ) [Equation 1]
Now, let's substitute the new frequency and length values into the formula to find the new length:
L_new = (1/2 * 523.3Hz) * sqrt(T/μ) [Equation 2]
To find the amount by which the string must be shortened, we can subtract the new length from the initial length:
Shortening amount = L_initial - L_new
To calculate the shortening amount, we need the values of T and μ, which are not provided in the question. These values depend on the properties of the string and would need to be given or obtained from additional information. Without those values, it is not possible to provide a specific numerical answer to your question, but the steps provided above outline the general approach needed to solve the problem.
To determine how much the string on a violin must be shortened to produce a higher fundamental tone, you can use the formula that relates the length of a string to its frequency. The formula is derived from the fundamental mode of vibration of a string, which states that the frequency of a string is inversely proportional to its length.
The formula is given by:
f = (v / 2L)
Where:
f = frequency of the string
v = speed of sound
L = length of the string
In this case, you are given the initial frequency (440Hz) and length (25.4cm) of the string, and you need to find the new length that will produce a frequency of 523.3Hz.
Rearranging the formula, we can solve for L:
L = v / (2f)
Now let's plug in the given values:
v = speed of sound (Assuming it to be around 343 m/s)
f = 440Hz (initial frequency)
L = (343 m/s) / (2 * 440 Hz)
Calculating this, we find:
L ≈ 0.389 m
So, the initial length of the string is approximately 0.389 meters.
To find the new length that will produce a frequency of 523.3Hz, we rearrange the formula again:
L = v / (2f)
Plugging in the new frequency (523.3Hz), we get:
L = (343 m/s) / (2 * 523.3 Hz)
Calculating this, we find:
L ≈ 0.328 m
So, the string must be shortened by approximately 0.061 meters (or 6.1 cm) to produce a fundamental tone of frequency 523.3Hz.
In summary, to solve the problem:
1. Use the formula f = (v / 2L) to calculate the initial length of the string.
2. Rearrange the formula as L = v / (2f) and plug in the new frequency to calculate the new length of the string.
3. Subtract the initial length from the new length to find the amount by which the string needs to be shortened.