Waves of amplitude 1.3 cm move along a 14-m long string that has a mass of 90 g and is under a tension of 18 N.If the average total energy of the waves in the string is 5 J,calculate the frequency of the waves.
A)21 Hz
B)811 Hz
C)129 Hz
D)92 Hz
E)256 Hz

Question

Quizplus · Accepted Answer

The velocity of the waves on the string can be found using the formula:

v = sqrt(T/μ)

where T is the tension, μ is the linear mass density (mass per unit length) of the string, and sqrt denotes the square root.

μ = m/L = 90 g / 14 m = 6.43 x 10^-3 kg/m

v = sqrt(18 N / 6.43 x 10^-3 kg/m) = 54.4 m/s

The energy of a wave on the string can be found using the formula:

E = 1/2 * (μ/L) * (Aω)^2

where A is the amplitude of the wave, ω is its frequency, and * denotes multiplication.

Solving for ω:

ω = sqrt(2E / (μAL^2))

ω = sqrt(2(5 J) / (6.43 x 10^-3 kg/m)(1.3 x 10^-2 m)(14 m)^2) = 129 Hz

Therefore, the frequency of the waves is 129 Hz.

Waves of Amplitude 1