a certain string vibrates in its fundamental frequency at 250 Hz. If the string is 15 cm long, what is the velocity of the wave in the string? What is the wavelength of the second harmonic frequency (the second wave which will fit into this length of string)?
10 second
1 second
0.5 second
1.10 second
To find the velocity of the wave in the string, we can use the equation:
v = f * λ
where:
v is the velocity of the wave,
f is the frequency, and
λ is the wavelength.
Since we are given the fundamental frequency (f = 250 Hz) and the length of the string (L = 15 cm), we can calculate the velocity.
First, let's convert the length of the string from centimeters to meters:
L = 15 cm = 0.15 m
Now, since the fundamental frequency corresponds to the first harmonic, the wavelength of the fundamental frequency can be found using the relationship:
λ = 2 * L
Substituting the value of L, we get:
λ = 2 * 0.15 m = 0.3 m
Next, we can rearrange the equation to solve for velocity:
v = f * λ
Substituting the given values, we get:
v = 250 Hz * 0.3 m = 75 m/s
Therefore, the velocity of the wave in the string is 75 m/s.
To find the wavelength of the second harmonic frequency, we can use the relationship:
λ_n = (2 * L) / n
where:
λ_n is the wavelength of the nth harmonic,
L is the length of the string, and
n is the harmonic number.
Since we are interested in the second harmonic (n = 2), we can substitute the values:
λ_2 = (2 * 0.15 m) / 2 = 0.15 m
Therefore, the wavelength of the second harmonic frequency is 0.15 m.