A 6.0 m wire with a mass of 50 g, is under tension. A transverse wave, for which the frequency is 810 Hz, the wavelength is 0.40 m, and the amplitude is 4.0 mm, is propagating on the wire. a) How long will it take for a crest of this wave to travel the length of the wire? b) What is the tension in the wire?

a) t = 0.0185 s = 18.5 ms

b) T = 874.8 N

Explanation:

a)

First we find the seed of wave:

v = fλ

where,

v = speed of wave

f = frequency = 810 Hz

λ = wavelength = 0.4 m

Therefore,

v = (810 Hz) (0.4 m)

v = 324 m/s

Now,

v = L/t

where,

L = length of wire = 6 m

t = time taken by wave to travel length of wire

Therefore,

324 m/s = 6 m/t

t = (6 m) / (324 m/s)

t = 0.0185 s = 18.5 ms

b)

From the formula of fundamental frquency, we know that:

Fundamental Frequency = v/2L = (1/2L) (√T/μ)

v = √ (T/μ)

where,

T = tension in string

μ = linear mass density of wire = m/L = 0.05 kg/6 m = 8.33 x 10⁻³ k gm⁻¹

Therefore,

324 m/s = √ (T/8.33 x 10⁻³ k gm⁻¹)

(324 m/s) ² = T/8.33 x 10⁻³ k gm⁻¹

T = 874.8 N