Question
The transverse displacement of a string (clamped at its two ends) is given by
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where x,y are in meter and t is in second. The length of the string is 1.5 m and its mass is 3.0 x 10–2kg. Answer the following:
(a) What are the wavelength, frequency and speed of propagation of each wave?
(b) Determine tension in the string.
Solution
(a) The transverse displacement of a string is given by,
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...(1)
The general wave equation of wave in the string clamped between two points is given by,
...(2)
where,
r is the amplitude of each wave superimposed.
On comparing (1) and (2), we get,
Angular frequency,
frquency, ![<pre>uncaught exception: <b>mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied</b><br /><br />in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56<br />#0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array)
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We know, v =
Therefore,
Speed of wave,
(b) We know speed of wave in the stretched string is given by,
...(1) The general wave equation of wave in the string clamped between two points is given by,
...(2) where,
r is the amplitude of each wave superimposed.
On comparing (1) and (2), we get,
Angular frequency,
frquency, We know, v =
Therefore,
Speed of wave,
(b) We know speed of wave in the stretched string is given by,
∴ 
where,
m is mass per unit length of wire.
It is given that mass of string is 3.0 x 10–2kg and length of string is 1.5 m.
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So,
Tension in the string is,
where,
m is mass per unit length of wire.
It is given that mass of string is 3.0 x 10–2kg and length of string is 1.5 m.
∴
So,
Tension in the string is,
