A transverse periodic wave on a string with a linear density of 0.200 kg/m is described by the following equation: y = 0.08 sin(469t - 28.0x), where x and y are in meters and t is in seconds. What is the tension in the string?
A)3.99 N
B)32.5 N
C)56.1 N
D)65.8 N
E)79.6 N

Question

Quizplus · Accepted Answer

The wave equation for a transverse wave on a string is:

v = sqrt(T/μ)

where v is the wave speed, T is the tension in the string, and μ is the linear density of the string (mass per unit length).

We can find the wave speed from the equation:

v = λf

where λ is the wavelength and f is the frequency. The frequency is given by the equation:

f = ω/2π

where ω is the angular frequency. The angular frequency is given by the coefficient of t in the equation for y:

ω = 469

The wavelength is given by:

λ = 2π/k

where k is the wave number. The wave number is given by the coefficient of x in the equation for y:

k = 28.0

Substituting these values into the equations gives:

f = ω/2π = 469/2π ≈ 74.5 Hz

λ = 2π/k = 2π/28.0 ≈ 0.224 m

v = λf = 0.224 × 74.5 ≈ 16.7 m/s

Finally, we can use the wave speed and linear density to find the tension:

T = μv^2 = 0.200 × 16.7^2 ≈ 56.1 N

Therefore, the answer is C.

A Transverse Periodic Wave on a String with a Linear