Question

The adjacent diagram shows three different modes of vibrations P, Q and R of the same string.
State the ratio of wavelengths of P and R.

Answer 1

Hint: To answer these types of questions you should be aware about the concept of wavelength which defines the distance between the points that are identical to a propagating waveform signal use the instructions to approach toward the solution and find the wavelength of the given waveforms.

Complete step-by-step solution -
To solve this question first let’s discuss about what is wavelength so the wavelength can be defined as the distance from similar points in the cycles of travelling waveform signals propagating in vacuum or any medium the wavelength is usually measured in meter, centimeter or millimeter.
So as we know that when a signal propagates in any medium or vacuum it waveforms which have crest and tough as shown in diagram given below so the wavelength is the distance between two crests or two troughs.

So for the vibration P we can say that it consist of 2 crest and 1 toughs occurring at the same time
Therefore by considering the diagram wavelength of P = $\dfrac{{3\lambda }}{2}$
For the vibration of R it consists of 1 crest and 1 tough
Therefore wavelength of R = $\dfrac{\lambda }{2}$
So the ratio of P and R is = ${\lambda _p}:{\lambda _R} = \dfrac{{3\lambda }}{2}:\dfrac{\lambda }{2}$
$\Rightarrow$ ${\lambda _p}:{\lambda _R} = 3:1$

Hence the ratio of modes of vibrations P and R is equals to 3: 1

Note: The concept of vibration that is mentioned in the above question can be explained as the phenomena in which when about an equilibrium the particles or any particle oscillates in to and fro motion it is called vibration for example when a pendulum oscillates about an equilibrium point. Frequency, amplitude and acceleration help in defining the momentum of vibration of any particle or body.