A wire 13.0 m long and having a mass of 80 g is stretched under a tension of 205 N. If two pulses, separated in time by 30.0 ms, are generated, one at each end of the wire, where will the pulses first meet?

To determine where the pulses will first meet, we need to calculate the wave speed of the wire based on its tension and mass. Once we have the wave speed, we can use the given time interval between the pulses to find the distance traveled by each pulse. The meeting point will be the sum of these distances.

1. Find the wave speed:
The wave speed is given by the equation v = sqrt(T/μ), where T is the tension and μ is the mass per unit length.
Tension (T) = 205 N
Mass (m) = 80 g = 0.08 kg
Length (L) = 13.0 m

Mass per unit length (μ) = m/L = 0.08 kg / 13.0 m = 0.0062 kg/m

Wave speed (v) = sqrt(T/μ) = sqrt(205 N / 0.0062 kg/m) ≈ 677 m/s

2. Calculate the distance traveled by each pulse:
Time interval (Δt) = 30.0 ms = 0.0300 s
Distance traveled by each pulse (d) = v * Δt
Distance traveled by each pulse = 677 m/s * 0.0300 s ≈ 20.3 m

3. Determine the meeting point of the pulses:
Since the pulses are generated at each end of the wire, they travel in opposite directions. Therefore, the meeting point will be the sum of the distances traveled by each pulse.
Meeting point = Distance traveled by first pulse + Distance traveled by second pulse
Meeting point = 20.3 m + 20.3 m = 40.6 m

Therefore, the pulses will first meet at a distance of 40.6 meters from one end of the wire.