Question
Derive an expression for the apparent frequency received by observer when alone observer is in motion. (Assume media to be at rest).
Solution
Let a source at rest be emitting the waves of frequency f and wavelength X.
When the observer is also at rest, he is receiving f waves in one second.
Now let the observer start moving with velocity u towards a stationary source.
When the observer starts moving with velocity u, he will receive waves
more than f.
Total number of waves received by observer in 1 second is,
![<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)
#1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493)
#2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs()
#3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...')
#4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array)
#5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array)
#6 {main}</pre>](/application/zrc/images/qvar/PHEN11040250-2.png)
Frequency is the number of waves received by the observer in 1 second.
Therefore, apparent frequency of wave received by observer,
If the observer moves away from the source, the observer will receive waves
less than f.
Therefore apparent frequency, when observer moves away is,
When the observer is also at rest, he is receiving f waves in one second.
Now let the observer start moving with velocity u towards a stationary source.
When the observer starts moving with velocity u, he will receive waves
more than f. Total number of waves received by observer in 1 second is,
Frequency is the number of waves received by the observer in 1 second.
Therefore, apparent frequency of wave received by observer,
If the observer moves away from the source, the observer will receive waves
less than f. Therefore apparent frequency, when observer moves away is,
