Warning: foreach() argument must be of type array|object, bool given in /var/www/html/web/app/themes/studypress-core-theme/template-parts/header/mobile-offcanvas.php on line 20

CP A police siren of frequency fsirenis attached to a vibrating platform. The platform and siren oscillate up and down in simple harmonic motion with amplitude APand frequency fp.(a) Find the maximum and minimum sound frequencies that you would hear at a position directly above the siren. (b) At what point in the motion of the platform is the maximum frequency heard? The minimum frequency? Explain.

Short Answer

Expert verified

A)The maximum and minifmum frequency are fLmax=fsirenvv2πfAandfLmin=fsirenvv+2πfA.

B)frequency is maximum at mean position and minimum at the edges.

Step by step solution

01

STEP 1: Simple Harmonic Motion

For an oscillatory motion, if the restoring force is directly proportional to the displacement of particle from its mean position. Thenthe motion is called simple harmonic motion.

02

The Maximum And Minimum Frequency

The maximum velocity of a system undergoing simple harmonic motion is vmax=2πfA

where vmaxis the maximum speed, f is the frequency and A is amplitude.

Frequency heard by the listener, directly over the siren, is

fL=fsvvvmax

Now,fLwill be maximum when the sign in the denominator is minus, which leads to

fLmax=fsirenvv2πfA

On the other hand,fL will be minimum when the sign in the denominator is plus, meaning a larger denominator, which leads to

fLmin=fsirenvv+2πfA

Therefore, the maximum frequency is detected when the platform reaches its maximum velocity and moving towards the listener, which happens when the platform is passing through the equilibrium position and moving up. In the same way, the minimum frequency is detected when the platform is at its edges, moving down.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

A person is playing a small flute 10.75cm long, open at one end and closed at the other, near a taut string having a fundamental frequency of 600.0Hz. If the speed of sound is 344.0m/s , for which harmonics of the flute will the string resonate? In each case, which harmonic of the string is in resonance?

If you wait at a railroad crossing as a train approach and passes, you hear a Doppler shift in its sound. But if you listen closely, you hear that the change in frequency is continuous; it does not suddenly go from one high frequency to another low frequency. Instead the frequency smoothly (but rather quickly) changes from high to low as the train passes. Why does this smooth change occur?

A sound wave in air at 20°C has a frequency of 320 Hz and a displacement amplitude of 5.00×10-3mmFor this sound wave calculate the (a) pressure amplitude (in Pa); (b) intensity W/m2(c) sound intensity level (in decibels).

In Example 16.18 (Section 16.8), suppose the police car is moving away from the warehouse at 20  m/s . What frequency does the driver of the police car hear reflected from the warehouse?

Small speakers A and B are driven in phase at 725 Hz by the same audio oscillator. Both speakers start out 4.50 m from the listener, but speaker A is slowly moved away (Fig. E16.34). (a) At what distance d will the sound from the speakers first produce destructive interference at the listener’s location? (b) If A is moved even farther away than in part (a), at what distance d will the speakers next produce destructive interference at the listener’s

See all solutions

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free