This figure shows a sinusoidal wave that is traveling from left to right, in the +x-direction. Assume that it is described by a frequency of 57.1 cycles per second, or hertz (Hz). 7.60 cm4.80 cm
A sinusoidal wave lies on an unlabeled coordinate system. One of the wave's maxima lies on the vertical axis. The horizontal distance from the first maximum to the first minimum is labeled 4.80 cm and the vertical distance between a maximum and a minimum is labeled 7.60 cm.
(a)
What is the wave's amplitude (in cm)?
cm
(b)
What is the wavelength (in cm)?
cm
(c)
Calculate the wave's period (in s).
s
(d)
Compute the speed of this wave (in m/s).
m/s

a)  A = 3.80 cm, b)   λ = 9.60 cm, c)  T = 1.75 10⁻² s, d)    v = 5.48 m / s

Explanation:

The wave is a way of transporting energy and moment without the need to transport the material. They are described by expressions of the type

           x = A sin (kx - wt)

where the amplitude A is the distance from the point of zero intensity to the maximum.

Frequency is the number of times the wave oscillates per unit of time

the wavelength is the distance necessary for the wave to start repeating.

a) In the exercise it tells us that the vertical distance from a machismo to a minimum that is worth 7.60 cm

when checking the definition of amplitude is from zero to a maximum, therefore the value given is twice the amplitude

          2A = 7.60

            A = 3.80 cm

b) the distance between a minimum and the next maximum is 4.80 cm

Using the definition of wavelength the given value corresponds to half wavelength

          λ/ 2 = 4.80

          λ = 9.60 cm

c) frequency and period are related

          f = 1 / T

          T = 1 / f

we calculate

           T = 1 / 57.1

           T = 0.0175 s

           T = 1.75 10⁻² s

d) the speed of the wave is related to the frequency and the wavelength

          v = λ f

          v = 0.0960 57.1

          v = 5.48 m / s

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