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

A 75.0-cm-long wire of mass 5.625 g is tied at both ends and adjusted to a tension of 35.0 N. When it is vibrating in its second overtone, find (a) the frequency and wavelength at which it is vibrating and (b) the frequency and wavelength of the sound waves it is producing.

Short Answer

Expert verified

The frequency and wavelength of the string is 136.6Hz and 0.5m respectively and the frequency and wavelength of the string is 136.6Hz and 2.518m respectively

Step by step solution

01

STEP 1 Concept of the frequency for standing wave for the strings fixed at both ends,

Thefrequency for standing wave for the strings is given asf=nv2Lwere,f is the frequency of nth harmonic, v is the velocity of the wave,nnthharmonic (n — 1, 3, 5, ...), L is the length of the pipe.

02

Calculate the frequency and wavelength of the string

For the string

μ=mL=5.625×10-30.75=7.5×10-3kg/mv=Fμ=35N7.5×10-3kg/m=68.313m/s

Second overtone is third harmonic n=3

f3=nv2L=3×65.32m/s2×0.75m=136.6Hzλ=vf=68.32136.6=0.5m

Therefore, the frequency and wavelength of the string is 136.6Hz and 0.5m respectively

03

Step 3 Calculate the frequency and wavelength of the sound

The string is the source of vibration, so, the sound has the same frequency 136.6Hz

λsound=vf=344136.6=2.518m

Therefore, the frequency and wavelength of the string is 136.6Hz and 2.518m respectively

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) If two sounds differ by 5.00 dB, find the ratio of the intensity of the louder sound to that of the softer one. (b) If one sound is 100 times as intense as another, by how much do they differ in sound intensity level (in decibels)? (c) If you increase the volume of your stereo so that the intensity doubles, by how much does the sound intensity level increase?

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?

Two guitarists attempt to play the same note of wavelength 64.8cm at the same time, but one of the instruments is slightly out of tune and plays a note of wavelength 65.2cm instead. What is the frequency of the beats these musicians hear when they play together?

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?

Can a standing wave be produced on a string by superposing two waves traveling in opposite directions with the same frequency but different amplitudes? Why or why not? Can a standing wave be produced by superposing two waves traveling in opposite directions with different frequencies but the same amplitude? Why or why not?

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