Question

A wave of frequency $500Hz$ travels between \[X\] and \[Y\] , a distance of $600m$ in $2\sec $. How many wavelengths are there in distance \[XY\] ?
A. $1000$
B. $300$
C. $180$
D. $2000$

Answer 1

Hint: According to the question, a wave travels between two points. So, we will first find the wavelength of this wave, which is the distance between its two consecutive troughs or crests. Then dividing the length of \[X\] and \[Y\], by the wavelength will give the number of wavelengths between \[XY\].


Complete answer:
Let us first write the information given in the question.
Frequency of the wave $f = 500Hz$, the wave travels between \[X\] and \[Y\] whose distance $s = 600m$is in time $t = 2\sec $.
Now, let us find the velocity first by the following formula.
$v = \dfrac{{dis\tan ce}}{{time}}$
Let us substitute the values.
$v = \dfrac{{600}}{2} = 300m/s$
Now following is the relation between wavelength, speed, and frequency of the wave.
$v = f\lambda $
Here, $v$is the velocity of the wave, $f$ is the frequency of the wave and, $\lambda $ is the wavelength.
Now let us substitute the values in the formula.
$300 = 500\lambda \Rightarrow \lambda = \dfrac{{300}}{{500}} = \dfrac{3}{5}m$
Let us now find the number of wavelengths in the distance of $600m$ by the following way.
Number of wavelengths $ = \dfrac{{600}}{{3/5}} = 1000$
Therefore, in between \[X\] and \[Y\] , $1000$ wavelengths will be present.
Hence, the correct option is (A) $1000$.

Note:
A wave is a disturbance created in the medium that can travel in the form of energy from one place to another, without the actual transfer of particles of the medium.
The speed of the waves is highest in air or vacuum and decreases in the denser medium. So, the speed of the wave will be more in the rarer medium as compared to the denser medium.