Question

A string 1m long is drawn by a 300Hz vibrator attached to its end. The string vibrates in three segments. The speed of transverse waves in the string is equal to

(A) $100m/s$

(B) $200m/s$

(C) $300m/s$

(D) $400m/s$

Answer 1

Hint: A transverse wave is defined as the moving wave whose oscillation is perpendicular to the direction of the wave or path of propagation. A simple example is given by the waves that can be made on the horizontal length of the string by anchoring one end and moving the other end.

In a transverse wave, the vibrations are at right angles to the direction of wave travel. The best example is vibrations in a guitar string

Complete step by step solution:

In question they have given the string length $l = 1m$ and they have also given the frequency that is $f = 300Hz$

Here we have given that string vibrated in 3 segment hence we can write as

$\dfrac{\lambda }{2} + \dfrac{\lambda }{2} + \dfrac{\lambda }{2} = l$

After simplifying the above equation we can write it as

$\dfrac{{3\lambda }}{2} = l$

Now we want the value of $\lambda$ so take it outside hence the equation becomes

$\lambda = \dfrac{{2l}}{3}$

As we know the formulae for the frequency that is

$f = \dfrac{V}{l}$

In the question they have asked the speed. Speed is nothing but velocity hence we can write the equation as

$V = f\lambda$

Now substitute the value of $\lambda$ and $f$ so we get

$V = 300 \times \dfrac{{2l}}{3}$

As we know the value of $l$ so after substituting that we get

$V = 300 \times \dfrac{{2(1)}}{3}$

After calculating the above equation we get

$V = 200m/s$

Hence, the correct answer is option (B).

Note: A vibration that occurs in an object must repeat a movement during the time interval. A wave is a disturbance that extends from one place to another through space. Light and sound are the vibrations that move through a space and they are waves! Properties of Vibrations. A pendulum swings in a periodic motion.