The distance between two consecutive nodes
of a standing wave is 19.2 cm. The hand generating
the pulses moves up and down through
a complete cycle 2.59 times every 7.44 s.
Find the velocity of the wave.
Answer in units of m/s.
The frequency is (2.59 / 7.44) Hertz and the wavelength is (0.192 * 2) m therefore you use the equation that states the Velocity = λf
Velocity = (2.59 / 7.44) * (0.192 * 2)
Velocity = 0.1336774194
Why did the wave go to therapy? Because it had some serious wavelength issues!
To find the velocity of the wave, we can use the formula:
velocity = frequency × wavelength
First, let's find the frequency. The hand generating the pulses moves up and down through a complete cycle 2.59 times every 7.44 s. So, the frequency can be calculated as:
frequency = number of cycles / time
= 2.59 / 7.44 s
Next, let's convert the distance between two consecutive nodes from centimeters to meters:
wavelength = 19.2 cm / 100 cm/m
Now, we can plug these values into the formula and calculate the velocity:
velocity = (2.59 / 7.44 s) × (19.2 cm / 100 cm/m)
Calculating this out, we get:
velocity ≈ 0.070 m/s
So, the velocity of the wave is approximately 0.070 m/s.
To solve this problem, we can use the formula for wave velocity:
Velocity (v) = Frequency (f) × Wavelength (λ)
First, let's find the frequency (f).
Frequency (f) is the number of complete cycles per second, so we divide the number of cycles by the time (in seconds):
f = (2.59 cycles) / (7.44 s) = 0.3489 Hz
Next, let's find the wavelength (λ).
The distance between two consecutive nodes of the standing wave is the length of half a wave, so we multiply the given distance by 2:
λ = 2 × 19.2 cm = 38.4 cm
Now, we have to convert the wavelength from centimeters (cm) to meters (m) since the velocity formula requires the wavelength to be in meters. There are 100 cm in 1 m, so:
λ = 38.4 cm / 100 = 0.384 m
Finally, we can substitute the values into the velocity formula to find the wave velocity:
v = f × λ = 0.3489 Hz × 0.384 m = 0.134m/s
Therefore, the velocity of the wave is 0.134 m/s.
To find the velocity of the wave, we need to use the formula:
velocity = frequency × wavelength
First, let's find the frequency of the wave. We know that the hand generating the pulses moves up and down through a complete cycle 2.59 times every 7.44 s. This means the frequency is the number of complete cycles per second:
frequency = 2.59 / 7.44
Next, let's find the wavelength of the wave. The distance between two consecutive nodes of a standing wave is given as 19.2 cm. However, we need to convert it to meters:
wavelength = 19.2 cm / 100
Now we can calculate the velocity:
velocity = frequency × wavelength
Substituting the values we found:
velocity = (2.59 / 7.44) × (19.2 cm / 100)
velocity = 0.348lowymeter/second
Therefore, the velocity of the wave is approximately 0.348 m/s.