Question

A harmonic wave is traveling along a rope. It is observed that the oscillator that generates the wave completes 37.0 vibrations in 33.0 s. Also, a given maximum travels 421 cm along the rope in 8.0 s. What is the wavelength?

Answer 1

0.472 m

Step-by-step explanation:

f = cycles/ second = 33 / 37 = 0.892 Hz

Vmean = Δx / Δt = 4.21m / 8s = 0.526

Vwave = λ x f

⇒ λ = f / Vwave = 0.526 / 0.892 = 0.472 m

Answer 2

0.47 m

Step-by-step explanation:

`N` = Number of vibrations = 37

`t` = total time taken = 33 s

`T` = time period of each vibration

frequency of vibration is given as

`f = (N)/(t) \\f = (37)/(33) \\f = 1.12` Hz

`d` = distance traveled along the rope = 421 cm = 4.21 m

`t` = time taken to travel the distance = 8 s

`v` = speed of the wave

Speed of the wave is given as

`v = (d)/(t)\\v = (4.21)/(8)\\v = 0.53 ms^(-1)`

`\lambda` = wavelength of the harmonic wave

wavelength of the harmonic wave is given as

`\lambda = (v)/(f) \\\lambda = (0.53)/(1.12) \\\lambda = 0.47 m`