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Sound — Science STD 9 — Question

Gujarat BoardEnglish MediumSTD 9ScienceSound3 Marks
Question
A device called oscillator is used to send waves along a stretched string. The string is $20\ cm$ long, and four complete waves fit along its length when the oscillator vibrates $30$ times per second. For the waves on the string:
  1. What is their wavelength?
  2. What is their frequency?
  3. What is their speed?
✓

Answer

  1. Given that there are four complete waves. So,
$\text{Wavelength}=\frac{\text{Total length of string}}{\text{Number of waves}}$
Therefore,
$\text{Wavelength}=\frac{20}{4}\text{cm}$
$=5\text{cm}$
$=0.05\text{m}$
  1. We have to calculate frequency. We know,
Frequency = (Vibration per second) $\times $ (Number of complete waves formed)
Therefore frequency,
Frequency $= (30) \times (4)Hz$
$= 120Hz$
  1. Now we have to calculate the velocity of the wave.
Given: Frequency $f = 120\ Hz$
Wavelength $\lambda=0.05\text{m}$
We know the relation between velocity, frequency, and wavelength
$\text{v}=\text{f}\times\lambda$
Where,
$ν$ is the velocity,
$f$ the frequency,
$\lambda$ the wavelength.
Therefore,
$ν = (120) \times (0.05)m/s$
$= 6m/s$
Therefore, velocity of the wave is $6\ m/s$.

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