Try the fastest way to create flashcards
Question

A piano tuner uses a 512-Hz tuning fork to tune a piano. He strikes the fork and hits a key on the piano and hears a beat frequency of 5 Hz. He tightens the string of the piano, and repeats the procedure. Once again he hears a beat frequency of 5 Hz. What happened?

Solution

Verified
Step 1
1 of 6

1 Concepts and Principles

1- The phenomenon of beating\textbf{beating} is the periodic variation in intensity at a given point due to the superposition of two waves having slightly different frequencies. The beat frequency is:

fbeat=f1f2\begin{gather*} f_{\text{beat}}=|f_1-f_2|\tag{1} \end{gather*}

where f1f_1 and f2f_2 are the frequencies of the individual waves.


2- Waves Under Boundary Conditions\textbf{Waves Under Boundary Conditions}: the boundary conditions determine which standing-wave frequencies are allowed. For waves on a string, there must be nodes at both ends. The wavelengths and natural frequencies of normal modes are given by:

fn=nv2L=n2LFTμ    n=1,  2,  3,  ...\begin{align*} f_n&=n\dfrac{v}{2L}=\dfrac{n}{2L}\sqrt{\dfrac{F_T}{\mu}}\;\;\quad\quad\quad\quad\quad \quad \quad \quad n=1,\;2,\;3,\;...\tag{2} \end{align*}

Create a free account to view solutions

Create a free account to view solutions

Recommended textbook solutions

Physics for Scientists and Engineers: A Strategic Approach with Modern Physics 4th Edition by Randall D. Knight

Physics for Scientists and Engineers: A Strategic Approach with Modern Physics

4th EditionISBN: 9780133942651 (8 more)Randall D. Knight
3,508 solutions
Mathematical Methods in the Physical Sciences 3rd Edition by Mary L. Boas

Mathematical Methods in the Physical Sciences

3rd EditionISBN: 9780471198260 (1 more)Mary L. Boas
3,355 solutions
Fundamentals of Physics 10th Edition by David Halliday, Jearl Walker, Robert Resnick

Fundamentals of Physics

10th EditionISBN: 9781118230718 (3 more)David Halliday, Jearl Walker, Robert Resnick
8,971 solutions
University Physics, Volume 1 1st Edition by Jeff Sanny, Samuel J Ling, William Moebbs

University Physics, Volume 1

1st EditionISBN: 9781938168277Jeff Sanny, Samuel J Ling, William Moebbs
1,471 solutions

More related questions

1/4

1/7