The distance between two nearest nodes of
a standing wave is 16.3 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.
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 are given that the hand generated pulses move up and down through a complete cycle four times every seven seconds. This means the frequency of the wave is 4 cycles per 7 seconds.
To find the wavelength, we can use the given information that the distance between two nearest nodes of the standing wave is 16.3 cm. The distance between two nearest nodes is equal to half a wavelength.
So, the wavelength can be calculated by doubling the distance between two nearest nodes:
wavelength = 2 × 16.3 cm = 32.6 cm
Now, we need to convert the wavelength from centimeters to meters, as the answer needs to be in m/s. Since 1 meter is equal to 100 centimeters, we divide the wavelength by 100:
wavelength = 32.6 cm ÷ 100 = 0.326 m
Now, we can calculate the velocity of the wave:
velocity = frequency × wavelength
velocity = (4 cycles/7 seconds) × (0.326 m/cycle)
Simplifying the expression:
velocity = 0.1857 m/s
Therefore, the velocity of the wave is approximately 0.1857 m/s.