105. A cable with a linear density of μ=0.2kg/m is hung from telephone poles. The tension in the cable is 500.00 N. The distance between poles is 20 meters. The wind blows across the line, causing the cable resonate. A standing waves pattern is produced that has 4.5 wavelengths between the two poles. The speed of sound at the current temperature T=20°C is 343.00m/s . What are the frequency and wavelength of the hum?

11.5 Hz, 29.83 m

Explanation:

Given

Linear density of the cable, μ = 0.2 kg/m

Tensión in the cables, T = 500 N

Wavelength of the wave, = 4.5 Waves

Distance between the poles, L = 20 m

Temperature of, t = 20° C

Speed of sound, v = 343 m/s

λ = length / number of waves =

λ = 20 / 4.5

λ = 4.44 m

Frequency of a standing wave is the same as frequency of a hum. Calculated using the formula

F = n/2L * √(T/μ)

F = 1/λ * √(T/μ)

F = 1/4.44 * √(500/0.2)

F = 0.23 * √2500

F = 0.23 * 50

F = 11.5 Hz

Wavelength of the hum,

λ = v/f

λ = 343 / 11.5

λ = 29.83 m

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