Question

A school is setting up for the science department's annual "Night of Phantastic Physics Phun." One of the most popular demonstrations is the traveling wave pulse, in which participants pluck one end of a long, taut wire to send transverse wave pulses racing across the room. The goal is for the pulses to travel across the 20.5 m wire in a time of about 0.500 s. The mass of a m long piece of the wire is known to be 0.555 kg. What should the tension in the wire be in order to achieve the desired wave speed? Tension:______N

Answer 1

To achieve the desired wave speed of the traveling wave pulse, the tension in the wire should be 922.6 N.

Step-by-step explanation:

To achieve the desired wave speed, we need to find the tension in the wire. The wave speed in a string is given by the formula:

v = √(T/μ)

Where v is the wave speed, T is the tension in the wire, and μ is the linear mass density of the wire. The linear mass density can be calculated using the formula:

μ = m/L

Where m is the mass of the wire and L is the length of the wire. Plugging in the given values, we can solve for T:

T = μv^2

Substituting the known values:

T = (0.555 kg / 20.5 m) * (20.5 m / 0.500 s)^2 = 0.555 kg * (41 m/s)^2 = 922.6 N

Therefore, the tension in the wire should be 922.6 N to achieve the desired wave speed.

Answer 2

The tension required in the wire to achieve the desired wave speed of 41 m/s is 931.35 N, calculated using the wave speed formula considering the wire's linear mass density.

Step-by-step explanation:

To calculate the required tension in a wire to achieve a certain wave speed, we can use the formula for the speed of a wave on a string, which is given by v = √(T/μ), where v is the wave speed, T is the tension, and μ (mu) is the linear mass density of the string. The linear mass density is the mass per unit length of the string.

In this case, the desired wave speed is 0.500 s across a 20.5 m wire, which gives us a wave speed of v = 20.5 m / 0.500 s = 41 m/s. The mass of a 1 m long piece of the wire is 0.555 kg, so the linear mass density is μ = 0.555 kg/m. We can rearrange the wave speed formula to solve for tension: T = v2μ = (41 m/s)2 × 0.555 kg/m = 931.35 N. Therefore, the tension should be 931.35 N to achieve the desired wave speed.