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 :
(a.) what is their wavelength?
(b.) what is their frequency?
(c.) what is their speed?

Answer 1

$\texttt{\color{olive}Answer \: (a) :-}$

Given :-

Length of string = 20 cm

Number of complete waves = 4

We know that :-

$\texttt{\color{olive}Wavelength \: = \: } \frac{\texttt{\color{hotpink}total \: length \: of \: string}}{\texttt{\color{hotpink}number \: of \: waves }}$

Which means :-

The wavelength of the waves on this string :-

$= \frac{\texttt{20}}{\texttt{4} }$

$=\texttt{ 5 \: cm}$

$= \texttt{\color{hotpink}0.05 \: m}$

Therefore, the wavelength of the waves formed on this string = 0.05 m

$\texttt{\color{olive}Answer (b) :- }$

Given :-

Number of vibration per second = 30

Total number of complete waves formed = 4

We know that :-

Frequency = Vibration per second × Total number of complete waves formed

Which means :-

The frequency of the waves on this string :-

$=\texttt{ (30)×(4) \: Hz}$

$= \texttt{\color{hotpink}120 \: Hz}$

Therefore, the frequency of these waves = 120 Hz

$\texttt{\color{olive}Answer (c) :- }$

Given :-

Frequency of these waves = 120

The wavelength of these waves = 0.05 m

We know that :-

$= \texttt{v = f × λ}$

Here v = velocity, f = frequency and, λ = wavelength

Which means :-

The speed (or velocity) of these waves :-

$=\texttt{(120) × (0.05 ) m/s }$

$= \texttt{ \color{hotpink}\: 6 \: m/s}$

Therefore, the speed( or velocity) of these waves = 6 m/s

Answer 2

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