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Waves — Physics STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 SciencePhysicsWaves3 Marks
Question
A transverse harmonic wave travelling on a string is described by $\text{y}(\text{x, t}) = 3.0\sin \Big[(36\text{t}+0.018\text{x})+\frac{\pi}{4}\Big]$ where x and y are in cm and t in sec. The positive direction of x is from left to right.
  1. What is its amplitude and frequency?
  2. What is the initial phase at the origin?
  3. What is the least distance between to successive crest in the wave?
✓

Answer

  1. Travelling wave speed $=\frac{\omega}{\text{k}}=\frac{36}{0.018}$

$=\frac{36}{18}\times10^3$

$=2\times10^3\text{cms}^{-1}$

It travels along the negatice x-axis or from right of left.

  1. Amplitude = 3cm

Frequency $=\frac{\omega}{2\pi}=\frac{36}{2\pi}$

$=\frac{18}{\pi}\text{Hz}$

  1. Initial phase $=\frac{\pi}{4}$
  2. Distabce betweeb successive crests $=\lambda =\frac{2\pi}{\text{k}}$

$=\frac{2\pi}{0.018}=3.5\text{m}$

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