Math Problem Statement

PHYSICS WAVE MOTION

  1. In an experiment on standing waves, a string 31 cm long is attached to the prong of an electrically driven tuning fork that oscillates perpendicular to the length of the string at a frequency of 60 Hz.

Solution

To solve this physics problem about standing waves on a string, we need to break it down step by step, paying attention to the parameters given and what needs to be calculated.

Known information:

  • Length of the string, L=31 cm=0.31 mL = 31 \, \text{cm} = 0.31 \, \text{m}
  • Frequency of oscillation, f=60 Hzf = 60 \, \text{Hz}
  • The tuning fork causes the string to oscillate in a way that can generate standing waves.

Step-by-Step Outline:

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Math Problem Analysis

Mathematical Concepts

Wave Motion
Frequency
Standing Waves
Harmonics

Formulas

v = fλ (wave speed equation)
v = √(T/μ) (wave speed on a string, where T is tension and μ is linear density)
λ = 2L/n (relationship between wavelength and string length for standing waves)

Theorems

Wave Equation

Suitable Grade Level

Grades 11-12

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