Question

A nylon guitar string has a linear density of 7.20 g/m and is under a
tension of 150 N. The fixed supports are distance D = 90.0 cm apart.
The string is oscillating in the standing wave pattern shown in figure.
Calculate the (a) speed. (b) wavelength and (c) frequency of the
traveling waves whose superposition gives this standing wave.​

Answer 1

a) Speed of the travelling waves whose superposition gives this standing wave is 144.33 m/sec

b) Wavelength of the travelling waves whose superposition gives this standing wave is 1.8 m

c) Frequency of the travelling waves whose superposition gives this standing wave is 80.1 Hz.

Given-

• Linear density of nylon guitar string = 7.20 g/m
• Tension = 150 N
• Distance (D) = 90 cm

We know that for a transverse wave on a string the wave speed can be given by-

V = $\sqrt{\frac{T}{P} }$ where ρ is the linear density.

V = (150 / 0.0072)^1/2 = 144.33 m/sec

Wavelength = 2 × 90 cm = 180 cm = 1.8 m

We know that f = V/ λ where V is the speed, f is the frequency and λ is the wavelength.

By substitution the values

f = 144.33 m/sec / 1.8 m

f = 80.1 Hz