The distance between two consecutive nodes
of a standing wave is 22 cm. The hand generating
the pulses moves up and down through
a complete cycle 3.89 times every 4.68 s.
Find the velocity of the wave.
Answer in units of m/s
To find the velocity of the wave, we can use the equation:
velocity = frequency * wavelength
First, we need to find the frequency of the wave. Frequency is the number of complete cycles (or periods) per second. In this case, we are given that the hand generating the pulses completes 3.89 cycles every 4.68 seconds.
frequency = number of cycles / time
frequency = 3.89 cycles / 4.68 s
frequency ≈ 0.8333 Hz
Next, we need to find the wavelength of the wave. Wavelength is the distance between two consecutive nodes of the standing wave. In this case, we are given that the distance between two consecutive nodes is 22 cm. However, we need to convert it to meters to be consistent with the unit of velocity (m/s).
wavelength = 22 cm = 22/100 m = 0.22 m
Now we can calculate the velocity of the wave using the equation:
velocity = frequency * wavelength
velocity = 0.8333 Hz * 0.22 m
velocity ≈ 0.183 m/s
Therefore, the velocity of the wave is approximately 0.183 m/s.
To find the velocity of the wave, we can use the formula:
Velocity (v) = Frequency (f) * Wavelength (λ)
First, let's calculate the frequency. The number of complete cycles (n) the hand moves through in a given time can be calculated using the formula:
n = (number of cycles) / (time)
Given that the hand completes 3.89 cycles every 4.68 seconds, we can substitute these values into the formula:
n = 3.89 cycles / 4.68 s ≈ 0.832 cycles/s
Next, we can calculate the wavelength using the formula:
Wavelength (λ) = Distance between nodes / Number of segments
Given that the distance between consecutive nodes is 22 cm (0.22 m), and there is one segment between two consecutive nodes, we have:
Wavelength (λ) = 0.22 m / 1 = 0.22 m
Now we can substitute the frequency and wavelength values into the velocity formula:
Velocity (v) = Frequency (f) * Wavelength (λ)
v = 0.832 cycles/s * 0.22 m
v ≈ 0.183 m/s
Therefore, the velocity of the wave is approximately 0.183 m/s.