The velocity of waves on a string is 97 m/s. If the frequency of standing waves is 476 Hz, how far apart are two adjacent nodes?
To find the distance between two adjacent nodes, we need to consider the relationship between the velocity of the waves, frequency, and the distance between nodes.
The velocity of a wave on a string can be calculated using the formula:
v = λ * f
Where:
v = velocity of the wave
λ = wavelength of the wave
f = frequency of the wave
In this case, we know the velocity (97 m/s) and the frequency (476 Hz), and we need to find the wavelength (distance between two adjacent nodes).
Rearranging the formula, we get:
λ = v / f
Substituting the given values, we have:
λ = 97 m/s / 476 Hz
Calculating this, we find:
λ ≈ 0.203 m
So, the distance between two adjacent nodes (wavelength) is approximately 0.203 meters.
To find the distance between two adjacent nodes on a string, you can use the formula:
Distance between nodes = λ/2
Where λ represents the wavelength.
The formula for the wavelength of a wave is:
λ = v / f
Where v represents the velocity of the wave and f represents the frequency of the wave.
In this case, we are given:
Velocity (v) = 97 m/s
Frequency (f) = 476 Hz
We can substitute these values into the formula to find the wavelength (λ):
λ = v / f
λ = 97 m/s / 476 Hz
Now we can find the distance between nodes by dividing the wavelength by 2:
Distance between nodes = λ / 2
Distance between nodes = (97 m/s / 476 Hz) / 2
Calculating that:
Distance between nodes ≈ 0.102 m or 10.2 cm
So, the distance between two adjacent nodes is approximately 0.102 meters (or 10.2 centimeters).