Question

The distance between two consecutive nodesof a standing wave is 20.9cm.Thehandgen-erating the pulses moves up and down throughacompletecycle2.57 times every 4.47 s.Find the velocity of the wave.

Answer 1

Answer:

Velocity, v = 0.239 m/s

Explanation:

Given that,

The distance between two consecutive nodes of a standing wave is 20.9 cm = 0.209 m

The hand generating the pulses moves up and down through a complete cycle 2.57 times every 4.47 s.

For a standing wave, the distance between two consecutive nodes is equal to half of the wavelength.

$\dfrac{\lambda}{2}=0.209\ m\\\\\lambda=0.418\ m$

Frequency is number of cycles per unit time.

$f=\dfrac{2.57}{4.47}\\\\f=0.574\ Hz$

Now we can find the velocity of the wave.

Velocity = frequency × wavelength

v = 0.574 × 0.418

v = 0.239 m/s

So, the velocity of the wave is 0.239 m/s.