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Chapter 17: Q42P (page 509)

A sound wave in a fluid medium is reflected at a barrier so that a standing wave is formed. The distance between nodes is 3.8cm, and the speed of propagation is1500m/s. Find the frequency of the sound wave.

Short Answer

Expert verified

The frequency of the wave is19737 Hz

Step by step solution

01

The given data

  1. Speed ofthe wave,v=1500m/s
  2. Distance between consecutive nodes,l=3.8 cmor0.038 m
02

Understanding the concept of nodes in oscillations

The distance between the consecutive nodes is half of the wavelength. Using this and the formula for the velocity of the wave in terms of frequency and wavelength, we can find the required quantity.

Formula:

The frequency of an oscillation, f=vλ …(i)

03

Determining the frequency

Distance between the two consecutive nodes is equal to half the wave length. Hence, the wavelength of the wave is given as:

l=λ2λ=2l=2(0.038 m)=0.076m

Again using equation (i), the frequency of the wave is given as:

f=1500 ms0.076 m=19736.8 Hz≈19737Hz

Hence, the value of the frequency is19737Hz

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