Transverse Wave Physics Example 4

Follow the full solution, then compare it with the other examples linked below.

Example 4

hard
A guitar string (μ=0.003 kg/m\mu = 0.003 \text{ kg/m}, length 0.65 m0.65 \text{ m}) is tuned to play a note at 330 Hz330 \text{ Hz} (fundamental mode). What tension must be applied to the string?

Solution

  1. 1
    In the fundamental mode, the string vibrates with a wavelength λ=2L=2×0.65=1.3 m\lambda = 2L = 2 \times 0.65 = 1.3 \text{ m}.
  2. 2
    Wave speed: v=fλ=330×1.3=429 m/sv = f\lambda = 330 \times 1.3 = 429 \text{ m/s}.
  3. 3
    Tension: T=μv2=0.003×4292=0.003×184041≈552 NT = \mu v^2 = 0.003 \times 429^2 = 0.003 \times 184041 \approx 552 \text{ N}.

Answer

T≈552 NT \approx 552 \text{ N}
Musical instruments rely on transverse standing waves. The tension must be precisely set to produce the desired frequency. Higher tension gives higher pitch for the same string length and density.

About Transverse Wave

A wave in which the particles of the medium oscillate perpendicular to the direction of wave propagation.

Learn more about Transverse Wave →

More Transverse Wave Examples

Example 1 easy

A transverse wave on a rope has a wavelength of [formula] and a frequency of [formula]. What is the

Example 2 medium

A transverse wave on a string has a speed of [formula]. The string has a tension of [formula]. What

Example 3 medium

Explain why transverse waves can travel through solids but not through fluids (liquids and gases). G

← All Transverse Wave Examples Transverse Wave Concept