A string is 2.4 m long, and the speed of sound along this string is 450 m/s. Calculate the frequency of the wave that would produce a first harmonic. Assume the string has nodes at both ends.
What I've Tried
Ln=2.4m
v= 450 m/s
f=?
n=2
Ln=(4-1)/4 * Wavelength
Wavelength = 2.4m/0.75m
=3.2m
Wavelength=v/f
f=v/wavelength
f=450 m/s / 3.2m
=140 hz.
The answer is 94 hz
well, if nodes at both ends then the wave is twice as long as the string, 4.8 meters (draw it with half a wave on the string and bulge in the middle)
how long does it take for 4/8 meters?
T = 4.8/450
so
f = 450/4.8 = 93.75 Hz which is 94 indeed
Well, your calculations may be a little off, but I'm here to help! Let's calculate the correct frequency together, shall we?
Given:
Length of the string (L) = 2.4 m
Speed of sound (v) = 450 m/s
Number of the harmonic (n) = 1 (first harmonic)
To find the frequency (f), we can use the formula:
f = (n * v) / (2 * L)
Plugging in the values:
f = (1 * 450 m/s) / (2 * 2.4 m)
Now, let's do the math:
f = 450 m/s / 4.8 m
f = 93.75 Hz
So, the correct frequency for the first harmonic in this case is approximately 93.75 Hz. Keep practicing those calculations, and you'll be a pro in no time!
To calculate the frequency of the wave that would produce a first harmonic, you need to consider the fact that the string has nodes at both ends.
In a string with nodes at both ends, the length of the string (Ln) is equal to half of the wavelength (λ/2) of the wave.
Given:
Ln = 2.4 m
v = 450 m/s
First, calculate the wavelength (λ) using the formula:
Ln = λ/2
Plug in the known values:
2.4 m = λ/2
Multiply both sides by 2:
4.8 m = λ
Now, use the relationship between the speed of sound (v), wavelength (λ), and frequency (f):
v = f * λ
Solve for f by rearranging the formula:
f = v/λ
Substitute the given values:
f = 450 m/s / 4.8 m
Calculate the frequency:
f ≈ 94 Hz
Therefore, the frequency of the wave that would produce a first harmonic is approximately 94 Hz.
To calculate the frequency of the wave that would produce a first harmonic on a string, we can use the formula:
f = (n * v) / (2 * L)
where:
f is the frequency of the wave,
n is the harmonic number (in this case, first harmonic corresponds to n=1),
v is the speed of sound along the string, and
L is the length of the string.
From the given information, we have:
L = 2.4 m (length of the string)
v = 450 m/s (speed of sound along the string)
n = 1 (first harmonic)
Substituting these values into the formula, we get:
f = (1 * 450 m/s) / (2 * 2.4 m)
f = 94 Hz
So, the frequency of the wave that would produce a first harmonic on the string is 94 Hz.