Question

A 7-m long wire with a mass of 40 g is under tension. A transverse wave for which the frequency is 630 Hz, the wavelength is 0.5 m, and the amplitude is 7.1 mm is propagating on the wire.
The maximum transverse acceleration of a point on a wire is closest to ____ m/s².

Answer 1

Answer:

111249.41m/s²

Explanation:

Mass of the wire m = 40g = 0.04 Kg

Length of the wire l = 7 m

Linear density of wire μ = m/l

= 0.04/7

= 0.0057 Kg/m

Frequency n = 630 Hz

Wavelength λ = 0.5 m

Amplitude A =  7.1mm = 0.0071m

Speed of the wave v = nλ

= 630*0.5

= 315 m/s

Angular speed ω = 2πn

= 2π*630

= 3958.40 rad/s

Maximum transeverse acceleration

a = ω^2 A

= 3958.40² × 0.0071m

= 111249.41m/s²