Question

A 8.0-m long wire with a mass of 10 g is under tension. A transverse wave for which the frequency is 570 Hz, the wavelength is 0.10 m, and the amplitude is 3.7 mm is propagating on the wire. The maximum transverse acceleration of a point on a wire is what? Show work. Answer is in m/s^2

Answer 1

To find the maximum transverse acceleration of a point on the wire, we can use the formula:

amax = (2πf)^2 * A

Where:

amax is the maximum transverse acceleration

f is the frequency of the wave

A is the amplitude of the wave

Given:

Frequency (f) = 570 Hz

Wavelength (λ) = 0.10 m

Amplitude (A) = 3.7 mm = 3.7 x 10^-3 m (converted to meters)

First, we need to find the wave speed (v) using the formula:

v = f * λ

Using the given values:

v = 570 Hz * 0.10 m

v = 57 m/s

Now, we can calculate the maximum transverse acceleration:

amax = (2πf)^2 * A

amax = (2π * 570 Hz)^2 * 3.7 x 10^-3 m

amax = (2π * 570)^2 * 3.7 x 10^-3 m

amax ≈ 19665.89 m/s^2

Therefore, the maximum transverse acceleration of a point on the wire is approximately 19665.89 m/s^2.

Step-by-step explanation: