Question

the d-string on a guitar has a linear mass density of 2.1 × 10-3 kg/m and an oscillating length of 0.62 m. it is stretched at a tension of 82.5 n. The guitarist plucks the D-string. At what speed, in meters per second, does the pulse travel along the string?

Answer 1

To calculate the speed of a pulse on a guitar string, use the square root of the tension divided by the linear mass density of the string. Applying this to the given D-string with relevant values, the pulse speed is approximately 198.21 m/s.

Step-by-step explanation:

The question involves calculating the speed of a pulse traveling along a guitar string given the linear mass density, the oscillating length of the string, and the tension applied to it. This type of problem is commonly found in physics, specifically in the area of waves and vibrations. The formula used to determine the wave speed v is given by:

v = √(T/μ),

where T is the tension in the string and μ (mu) is the linear mass density. For the given D-string of a guitar, with a linear mass density of 2.1 × 10-3 kg/m and tension of 82.5 N, the calculation would be:

v = √(82.5 N / (2.1 × 10-3 kg/m))

We then compute the square root of the tension divided by the linear mass density to find the pulse propagation speed.

v = √(82.5 / 0.0021)
= √(39285.7142857)

So, the pulse travels down the string at approximately 198.21 m/s.