A rope is stretched with a tension of 248 N. The rope is of length 12.5 m with a mass of 161 g. Two pulses are formed at opposite ends of the rope, separated in time by 30.1 ms. Determine how far from the farther end of the rope the pulses will first meet?

speed of wave=sqrt(tension*length/mass)

To find the distance from the farther end of the rope where the pulses will first meet, we need to use the wave equation:

v = √(T/μ)

where:
v is the velocity of the wave,
T is the tension in the rope,
and μ is the linear mass density of the rope.

1. First, let's calculate the linear mass density of the rope:
μ = (mass of the rope) / (length of the rope)

mass of the rope = 161 g = 0.161 kg
length of the rope = 12.5 m

μ = 0.161 kg / 12.5 m

2. Next, we can calculate the velocity of the wave using the given tension:
v = √(T / μ)

T = 248 N
μ = 0.161 kg / 12.5 m

v = √(248 N / (0.161 kg / 12.5 m))

3. Once we have the velocity of the wave, we can determine the distance the first pulse travels in 30.1 ms (or 0.0301 seconds):

distance = velocity × time

distance = v × t
= (√(248 N / (0.161 kg / 12.5 m))) × 0.0301 s

Simply plug in the values and calculate to find the distance.