The distance between two nearest nodes of
a standing wave is 17.3 cm. Hand generated
pulses move up and down through a complete
cycle four times every seven seconds.
Find the velocity of the wave.
Answer in units of m/s.
frequency=4cycles/7seconds
velocity=frequency*wavelength
= 4/7 * 2*17.3 cm/sec change to m/s
19.77
To find the velocity of the wave, we can use the formula:
Velocity = Frequency x Wavelength
First, let's find the frequency of the wave using the given information. The question states that hand-generated pulses move up and down through a complete cycle four times every seven seconds.
Frequency = Number of cycles / Time
Frequency = 4 cycles / 7 seconds
Next, we need to find the wavelength of the wave. The question states that the distance between two nearest nodes of a standing wave is 17.3 cm. In a standing wave, the distance between two nearest nodes is one-half of a wavelength.
Wavelength = 2 x Distance between nearest nodes
Wavelength = 2 x 17.3 cm
Now, let's convert the wavelength from centimeters to meters (as the answer requires it to be in m/s).
Wavelength = (2 x 17.3 cm) / 100 (to convert cm to m)
Finally, we can calculate the velocity:
Velocity = Frequency x Wavelength
Substitute the values:
Velocity = (4 cycles / 7 seconds) x (2 x 17.3 cm / 100)
Calculate the frequency and convert the wavelength:
Velocity = (4 / 7) x (2 x 0.173 m)
Simplify the equation:
Velocity = 8 x 0.173 m / 7
Calculate:
Velocity = 1.97114 m/s
Therefore, the velocity of the wave is approximately 1.97114 m/s.