Question

A wave on a string is described by

D(x,t)=(3.6cm)× sin[2π(x/(4.8m)+t/(0.14s)+1)], where x is in m and t is in s.

what is wave speed, frequency and wave number?

also:
At t=0.42s, what is the displacement of the string at x=5.2m

thanks!

Answer 1

The wave speed is 45.12 m/s, the frequency is 7.14 Hz, and the wave number is 1.31 mμ. At t=0.42s and x=5.2m, the displacement of the string is 1.8cm.

Step-by-step explanation:

The wave function D(x,t) can be written as D(x,t) = (3.6 cm) x sin[2π(x/(4.8 m) + t/(0.14 s) + 1)].

The wave speed can be calculated using the formula v = ω/k, where ω is the angular frequency and k is the wave number. In this case, the wave speed is v = 2π/0.14 = 45.12 m/s.

The frequency of the wave can be found using the formula f = ω/2π. In this case, the frequency is f = 1/0.14 = 7.14 Hz.

The wave number can be calculated using the formula k = 2π/λ. In this case, the wave number is k = 2π/4.8 = 1.31 mμ

At t = 0.42 s and x = 5.2 m, the displacement of the string can be calculated by substituting these values into the wave function. The displacement is D(x,t) = (3.6 cm) x sin[2π((5.2 m)/(4.8 m) + (0.42 s)/(0.14 s) + 1)] = 1.8 cm.

Answer 2

We are given an equation which describes a wave on a string:

D(x,t) = 3.6cm * sin[2π (x/4.8m) + t/(0.14s) + 1)]

where x is in meters
t is in seconds

at t = 0.42 seconds, and x = 5.2 m

First, convert the term into the equation with cm units:

D(x,t) = 3.6cm/100cm/m * sin[2π (x/4.8m) + t/(0.14s) + 1)]

then, substitute the values of x and t

D(x,t) = 3.6cm/100cm/m * sin[2π (5.2/4.8m) + 0.42/(0.14s) + 1)]

Solve for D, this is your displacement at x = 5.2 and at 0.42 seconds