The distance between two nearest nodes of a standing wave is 22.9 cm. Hand generated pulses move up and down through a complete cycle five times every seven seconds. Find the velocity of the wave. Answer in units of m/s
To find the velocity of the wave, we can use the formula:
Velocity = (Wavelength) x (Frequency)
The wavelength is the distance between two nearest nodes, which is given as 22.9 cm (or 0.229 m).
The frequency can be calculated by dividing the number of complete cycles by the time taken.
The number of complete cycles is given as five.
The time taken for these five cycles is seven seconds.
Frequency = (Number of complete cycles) / (Time taken)
Frequency = 5 / 7 Hz
Now, we can substitute the values back into the formula:
Velocity = (Wavelength) x (Frequency)
Velocity = 0.229 m x (5 / 7 Hz)
Calculating the expression:
Velocity = 0.229 m x (5 / 7 Hz)
Velocity = 0.1643 m/s
Therefore, the velocity of the wave is approximately 0.1643 m/s.
To find the velocity of the wave, we need to use the equation:
velocity = frequency × wavelength
Frequency is the number of complete cycles per second, and wavelength is the distance between two nearest nodes.
Given:
Frequency = 5 cycles / 7 seconds
Wavelength = 22.9 cm = 0.229 m
First, we need to find the frequency:
Frequency = Number of cycles / Time
Frequency = 5 cycles / 7 seconds
Next, we can use the equation:
Velocity = Frequency x Wavelength
Substituting the given values:
Velocity = (5/7) cycles/second x 0.229 m
Calculating the velocity:
Velocity = 0.32857 cycles/second x 0.229 m
Velocity ≈ 0.0750953 m/s
Therefore, the velocity of the wave is approximately 0.075 m/s.