The number of AM broadcasting stations that can be accommodated in a 100 kHz bandwidth if the highest frequency modulating a carrier is 5 kHz are
(A) 5
(B) 7
(C) 20
(D) 10

Hint: Bandwidth is basically the total space which can be allotted with carrier waves. A wave being modulated will produce the same frequency of lower and upper bands. So, we will need double space in the bandwidth to accommodate that wave.

 Complete step by step solution
Given: Bandwidth (B.W.) = 100 kHz
 \[{f_m}\] = Highest modulation frequency = 5 kHz
We know,
 $B.W. = 2n{f_m}$ ……(i)
Where, B.W. = Bandwidth.
     n = Number of AM broadcasting stations.
      \[{f_m}\] = Highest modulation frequency.
Putting the value of B.W. and \[{f_m}\] in equation (i) we get
 $100kHz = 2n \times 5kHz$
Cross multiplying, we get
$n = \dfrac{{100}}{{10}} = 10$ .

  (Option D)

 Additional information:
The need for modulating a wave are as follows-
(i) In case of direct transmission there is a possibility of signals from different stations getting lost or mixed up.
(ii) Direct transmission requires an antenna of abnormal size.
(iii) It is limited to only a short distance.

Note above formula gives the maximum number amplitude modulated broadcasting stations in a given bandwidth. There are three types of modulation
(i) Amplitude modulation: In this case the amplitude of a high frequency wave is varied in accordance with the instantaneous value of a low frequency signal. The high frequency wave is called a carrier wave and the low frequency wave is called the modulating voltage.
(ii) Frequency modulation: In this case the frequency of the carrier wave is varied in accordance with the instantaneous value of the modulating signal. This is advantageous because all man made and atmospheric disturbances cause variation in the amplitude to the carrier wave which is eliminated in case of frequency modulation.
(iii) Phase modulation: In this case the phase of the carrier wave is varied in accordance with the instantaneous value of the modulating signal.