Q59PP - University Physics with Modern Physics

Question

The professor again returns the apparatus to its original setting, so you again hear the original loud tone. She then slowly moves one speaker away from you until it reaches a point at which you can no longer hear the tone. If she has moved the speaker by 0.34 m (farther from you), what is the frequency of the tone? (a) 1000 Hz; (b) 2000 Hz; (c) 500 Hz; (d) 250 Hz.

Step-by-Step Solution

Answer

The frequency of the tone is 500 Hz .

Step 1: Important Concepts

Constructive interference occurs at a point where the superposing waves are in phase and destructive interference occurs at points where the two waves are out of phase.

Step 2: Application

Since you hear nothing, it is easy to conclude that the speakers have been moved in such a way that the sound interferes destructively 

Hence

                                               $$\begin{gathered} \frac{\lambda }{2}=0.34\hspace{0.33em}m \\ \lambda =0.68\hspace{0.33em}m \end{gathered}$$              

 

We know that the speed of the wave is given by 

                                             $v_s=\lambda f$                

Solving for f

                                                $f=\frac{v_s}{\lambda }$             

Plug the values to get

 

                                             $$\begin{gathered} f=\frac{340 m/s}{0.68 m } \\ =500 Hz \end{gathered}$$                

 

Hence, the correct option is C.