Vibrating a long spring with a succession of pulses with a frequency of 50hz produces adjecent nodes that are separated by 3.5cm. What is the velocity of the longitudinal waves formed?
f*lambda=v
nodes are at successive half wavelengths...
f*7.0cm=speed
solve for speed, f=50 hz
velocity = lamda * fequency
v= (.035)*(50)
v= 1.75 m/s
To find the velocity of the longitudinal waves formed, we can use the formula:
v = f * λ
where:
v = velocity of the wave
f = frequency of the wave
λ = wavelength of the wave
In this case, the frequency of the pulses is given as 50 Hz. We need to find the wavelength of the wave to calculate the velocity.
The distance between adjacent nodes is equal to half the wavelength (λ/2). In this case, it is given as 3.5 cm.
So, λ/2 = 3.5 cm
To find the wavelength itself, we multiply both sides of the equation by 2:
λ = 2 * 3.5 cm
λ = 7 cm
Now we have the frequency (f = 50 Hz) and the wavelength (λ = 7 cm). We can substitute these values into the velocity formula to find the velocity (v):
v = f * λ
v = 50 Hz * 7 cm
To calculate the velocity, we need to ensure that the units are consistent. The wavelength is currently in centimeters, but it's usually more convenient to work with meters when dealing with waves. So, let's convert centimeters to meters:
1 cm = 0.01 m
λ = 7 cm * 0.01 m/cm
λ = 0.07 m
Now we can calculate the velocity:
v = 50 Hz * 0.07 m
v ≈ 3.5 m/s
Therefore, the velocity of the longitudinal waves formed by vibrating the spring with a succession of pulses at a frequency of 50 Hz is approximately 3.5 m/s.