A harmonic wave in a wire has amplitude A = 7.6 mm, wavelength λ = 0.679 m and frequency f = 543 Hz.
What is the propagation speed of the wave? Answer in units of m/s.
The wire has linear mass density of 5.04 g/m.
Determine the wire’s tension. Answer in units of N.
To find the propagation speed of the wave, we can use the equation:
v = λ * f
where v is the propagation speed, λ is the wavelength, and f is the frequency.
Given:
Amplitude (A) = 7.6 mm = 7.6 * 10^-3 m
Wavelength (λ) = 0.679 m
Frequency (f) = 543 Hz
Substituting the values into the equation, we get:
v = 0.679 m * 543 Hz
Calculating this, we find:
v = 368.597 m/s (rounded to three decimal places)
Therefore, the propagation speed of the wave is 368.597 m/s.
To determine the wire's tension, we can use the equation for the wave speed on a string:
v = √(T/μ)
where v is the propagation speed, T is the tension in the wire, and μ is the linear mass density of the wire.
Given:
Propagation speed (v) = 368.597 m/s
Linear mass density (μ) = 5.04 g/m = 5.04 * 10^-3 kg/m (converting grams to kilograms)
Substituting the values into the equation, we can solve for T:
368.597 m/s = √(T/(5.04 * 10^-3 kg/m))
Squaring both sides of the equation, we get:
(368.597 m/s)^2 = T/(5.04 * 10^-3 kg/m)
Simplifying further, we find:
T = (368.597 m/s)^2 * (5.04 * 10^-3 kg/m)
Calculating this, we find:
T = 6787.334 N (rounded to three decimal places)
Therefore, the wire's tension is 6787.334 N.