|
135. Problem 19.43 (RHK) Vibrations from a 622-Hz tuning fork set up
standing waves in a string clamped at both ends. The wave speed for the string
is
|
. The
standing wave has four loops and is formed by superposition of waves of
amplitude 1.90 mm. We have to find (a) the length of the string;
(b) equation for the displacement of the string as a function of position and
time.
|
Solution: Click For PDF Version Frequency of the tuning fork,
Wave speed for the string,
Travelling waves generated in the string by the vibrations of the tuning fork
superpose to produce standing waves. Wavelength
As the standing wave in the string has four loops, the length of the string
Therefore, L = 1.248 m. Equation of standing waves formed out of travelling wave given by the functions
is given by
It is
We now work out the numerical values of variables in the above function.
The equation of the standing wave is
where x and y are in meter and t is in second.
|
.
.
and frequency f determine the speed v, 
.
