A device called oscillator is used to send waves along a stretche… - Vidyadip

Question

A device called oscillator is used to send waves along a stretched string. The string is $20cm$ long, and four complete waves fit along its length when the oscillator vibrates $30$ times per second. For the waves on the string:

What is their wavelength$?$
What is their frequency$?$
What is their speed$?$

✓

Answer

Given that there are four complete waves. So,

$\text{Wavelength}=\frac{\text{Total length of string}}{\text{Number of waves}}$
Therefore,
$\text{Wavelength}=\frac{20}{4}\text{cm}$
$=5\text{cm}$
$=0.05\text{m}$

We have to calculate frequency. We know,

Frequency $= ($Vibration per second$) × ($Number of complete waves formed$)$
Therefore frequency,
Frequency $= (30) × (4)Hz$
$= 120Hz$

Now we have to calculate the velocity of the wave.

Given: Frequency $f = 120Hz$
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,
$ν = (120) × (0.05)m/s$
$= 6m/s$
Therefore, velocity of the wave is $6m/s.$

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